Tag Archives: neuromorphic engineering

Connecting biological and artificial neurons (in UK, Switzerland, & Italy) over the web

Caption: The virtual lab connecting Southampton, Zurich and Padova. Credit: University of Southampton

A February 26, 2020 University of Southampton press release (also on EurekAlert) describes this work,

Research on novel nanoelectronics devices led by the University of Southampton enabled brain neurons and artificial neurons to communicate with each other. This study has for the first time shown how three key emerging technologies can work together: brain-computer interfaces, artificial neural networks and advanced memory technologies (also known as memristors). The discovery opens the door to further significant developments in neural and artificial intelligence research.

Brain functions are made possible by circuits of spiking neurons, connected together by microscopic, but highly complex links called ‘synapses’. In this new study, published in the scientific journal Nature Scientific Reports, the scientists created a hybrid neural network where biological and artificial neurons in different parts of the world were able to communicate with each other over the internet through a hub of artificial synapses made using cutting-edge nanotechnology. This is the first time the three components have come together in a unified network.

During the study, researchers based at the University of Padova in Italy cultivated rat neurons in their laboratory, whilst partners from the University of Zurich and ETH Zurich created artificial neurons on Silicon microchips. The virtual laboratory was brought together via an elaborate setup controlling nanoelectronic synapses developed at the University of Southampton. These synaptic devices are known as memristors.

The Southampton based researchers captured spiking events being sent over the internet from the biological neurons in Italy and then distributed them to the memristive synapses. Responses were then sent onward to the artificial neurons in Zurich also in the form of spiking activity. The process simultaneously works in reverse too; from Zurich to Padova. Thus, artificial and biological neurons were able to communicate bidirectionally and in real time.

Themis Prodromakis, Professor of Nanotechnology and Director of the Centre for Electronics Frontiers at the University of Southampton said “One of the biggest challenges in conducting research of this kind and at this level has been integrating such distinct cutting edge technologies and specialist expertise that are not typically found under one roof. By creating a virtual lab we have been able to achieve this.”

The researchers now anticipate that their approach will ignite interest from a range of scientific disciplines and accelerate the pace of innovation and scientific advancement in the field of neural interfaces research. In particular, the ability to seamlessly connect disparate technologies across the globe is a step towards the democratisation of these technologies, removing a significant barrier to collaboration.

Professor Prodromakis added “We are very excited with this new development. On one side it sets the basis for a novel scenario that was never encountered during natural evolution, where biological and artificial neurons are linked together and communicate across global networks; laying the foundations for the Internet of Neuro-electronics. On the other hand, it brings new prospects to neuroprosthetic technologies, paving the way towards research into replacing dysfunctional parts of the brain with AI [artificial intelligence] chips.”

I’m fascinated by this work and after taking a look at the paper, I have to say, the paper is surprisingly accessible. In other words, I think I get the general picture. For example (from the Introduction to the paper; citation and link follow further down),

… To emulate plasticity, the memristor MR1 is operated as a two-terminal device through a control system that receives pre- and post-synaptic depolarisations from one silicon neuron (ANpre) and one biological neuron (BN), respectively. …

If I understand this properly, they’ve integrated a biological neuron and an artificial neuron in a single system across three countries.

For those who care to venture forth, here’s a link and a citation for the paper,

Memristive synapses connect brain and silicon spiking neurons by Alexantrou Serb, Andrea Corna, Richard George, Ali Khiat, Federico Rocchi, Marco Reato, Marta Maschietto, Christian Mayr, Giacomo Indiveri, Stefano Vassanelli & Themistoklis Prodromakis. Scientific Reports volume 10, Article number: 2590 (2020) DOI: https://doi.org/10.1038/s41598-020-58831-9 Published 25 February 2020

The paper is open access.

Second order memristor

I think this is my first encounter with a second-order memristor. An August 28, 2019 news item on Nanowerk announces the research (Note: A link has been removed),

Researchers from the Moscow Institute of Physics and Technology [MIPT} have created a device that acts like a synapse in the living brain, storing information and gradually forgetting it when not accessed for a long time. Known as a second-order memristor, the new device is based on hafnium oxide and offers prospects for designing analog neurocomputers imitating the way a biological brain learns.

An August 28, 2019 MIPT press release (also on EurekAlert), which originated the news item, provides an explanation for neuromorphic computing (analog neurocomputers; brainlike computing), the difference between a first-order and second-order memristor, and an in depth view of the research,

Neurocomputers, which enable artificial intelligence, emulate the way the brain works. It stores data in the form of synapses, a network of connections between the nerve cells, or neurons. Most neurocomputers have a conventional digital architecture and use mathematical models to invoke virtual neurons and synapses.

Alternatively, an actual on-chip electronic component could stand for each neuron and synapse in the network. This so-called analog approach has the potential to drastically speed up computations and reduce energy costs.

The core component of a hypothetical analog neurocomputer is the memristor. The word is a portmanteau of “memory” and “resistor,” which pretty much sums up what it is: a memory cell acting as a resistor. Loosely speaking, a high resistance encodes a zero, and a low resistance encodes a one. This is analogous to how a synapse conducts a signal between two neurons (one), while the absence of a synapse results in no signal, a zero.

But there is a catch: In an actual brain, the active synapses tend to strengthen over time, while the opposite is true for inactive ones. This phenomenon known as synaptic plasticity is one of the foundations of natural learning and memory. It explains the biology of cramming for an exam and why our seldom accessed memories fade.

Proposed in 2015, the second-order memristor is an attempt to reproduce natural memory, complete with synaptic plasticity. The first mechanism for implementing this involves forming nanosized conductive bridges across the memristor. While initially decreasing resistance, they naturally decay with time, emulating forgetfulness.

“The problem with this solution is that the device tends to change its behavior over time and breaks down after prolonged operation,” said the study’s lead author Anastasia Chouprik from MIPT’s Neurocomputing Systems Lab. “The mechanism we used to implement synaptic plasticity is more robust. In fact, after switching the state of the system 100 billion times, it was still operating normally, so my colleagues stopped the endurance test.”

Instead of nanobridges, the MIPT team relied on hafnium oxide to imitate natural memory. This material is ferroelectric: Its internal bound charge distribution — electric polarization — changes in response to an external electric field. If the field is then removed, the material retains its acquired polarization, the way a ferromagnet remains magnetized.

The physicists implemented their second-order memristor as a ferroelectric tunnel junction — two electrodes interlaid with a thin hafnium oxide film (fig. 1, right). The device can be switched between its low and high resistance states by means of electric pulses, which change the ferroelectric film’s polarization and thus its resistance.

“The main challenge that we faced was figuring out the right ferroelectric layer thickness,” Chouprik added. “Four nanometers proved to be ideal. Make it just one nanometer thinner, and the ferroelectric properties are gone, while a thicker film is too wide a barrier for the electrons to tunnel through. And it is only the tunneling current that we can modulate by switching polarization.”

What gives hafnium oxide an edge over other ferroelectric materials, such as barium titanate, is that it is already used by current silicon technology. For example, Intel has been manufacturing microchips based on a hafnium compound since 2007. This makes introducing hafnium-based devices like the memristor reported in this story far easier and cheaper than those using a brand-new material.

In a feat of ingenuity, the researchers implemented “forgetfulness” by leveraging the defects at the interface between silicon and hafnium oxide. Those very imperfections used to be seen as a detriment to hafnium-based microprocessors, and engineers had to find a way around them by incorporating other elements into the compound. Instead, the MIPT team exploited the defects, which make memristor conductivity die down with time, just like natural memories.

Vitalii Mikheev, the first author of the paper, shared the team’s future plans: “We are going to look into the interplay between the various mechanisms switching the resistance in our memristor. It turns out that the ferroelectric effect may not be the only one involved. To further improve the devices, we will need to distinguish between the mechanisms and learn to combine them.”

According to the physicists, they will move on with the fundamental research on the properties of hafnium oxide to make the nonvolatile random access memory cells more reliable. The team is also investigating the possibility of transferring their devices onto a flexible substrate, for use in flexible electronics.

Last year, the researchers offered a detailed description of how applying an electric field to hafnium oxide films affects their polarization. It is this very process that enables reducing ferroelectric memristor resistance, which emulates synapse strengthening in a biological brain. The team also works on neuromorphic computing systems with a digital architecture.

MIPT has provided this image illustrating the research,

Caption: The left image shows a synapse from a biological brain, the inspiration behind its artificial analogue (right). The latter is a memristor device implemented as a ferroelectric tunnel junction — that is, a thin hafnium oxide film (pink) interlaid between a titanium nitride electrode (blue cable) and a silicon substrate (marine blue), which doubles up as the second electrode. Electric pulses switch the memristor between its high and low resistance states by changing hafnium oxide polarization, and therefore its conductivity. Credit: Elena Khavina/MIPT Press Office

Here’s a link to and a citation for the paper,

Ferroelectric Second-Order Memristor by Vitalii Mikheev, Anastasia Chouprik, Yury Lebedinskii, Sergei Zarubin, Yury Matveyev, Ekaterina Kondratyuk, Maxim G. Kozodaev, Andrey M. Markeev, Andrei Zenkevich, Dmitrii Negrov. ACS Appl. Mater. Interfaces 2019113532108-32114 DOI: https://doi.org/10.1021/acsami.9b08189 Publication Date:August 12, 2019 Copyright © 2019 American Chemical Society

This paper is behind a paywall.

Memristor-based neural network and the biosimilar principle of learning

Once you get past the technical language (there’s a lot of it), you’ll find that they make the link between biomimicry and memristors explicit. Admittedly I’m not an expert but if I understand the research correctly, the scientists are suggesting that the algorithms used in machine learning today cannot allow memristors to be properly integrated for use in true neuromorphic computing and this work from Russia and Greece points to a new paradigm. If you understand it differently, please do let me know in the comments.

A July 12, 2019 news item on Nanowerk kicks things off (Note: A link has been removed),

Lobachevsky University scientists together with their colleagues from the National Research Center “Kurchatov Institute” (Moscow) and the National Research Center “Demokritos” (Athens) are working on the hardware implementation of a spiking neural network based on memristors.

The key elements of such a network, along with pulsed neurons, are artificial synaptic connections that can change the strength (weight) of connection between neurons during the learning (Microelectronic Engineering, “Yttria-stabilized zirconia cross-point memristive devices for neuromorphic applications”).

For this purpose, memristive devices based on metal-oxide-metal nanostructures developed at the UNN Physics and Technology Research Institute (PTRI) are suitable, but their use in specific spiking neural network architectures developed at the Kurchatov Institute requires demonstration of biologically plausible learning principles.

Caption: Cross-section image of the metal-oxide-metal memristive structure based on ZrO2(Y) polycrystalline film (a); corresponding schematic view of the cross-point memristive device (b); STDP dependencies of memristive device conductance changes for different delay values between pre- and postsynaptic neuron spikes (c); photographs of a microchip and an array of memristive devices in a standard cermet casing (d); the simplest spiking neural network architecture learning on the basis of local rules for changing memristive weights (e). Credit: Lobachevsky University

A July 12, 2019 (?) Lobachevsky University press release (also on EurekAlert), which originated the news item, delves further into the work,

The biological mechanism of learning of neural systems is described by Hebb’s rule, according to which learning occurs as a result of an increase in the strength of connection  (synaptic weight) between simultaneously active neurons, which indicates the presence of a causal relationship in their excitation. One of the clarifying forms of this fundamental rule is plasticity, which depends on the time of arrival of pulses (Spike-Timing Dependent Plasticity – STDP).

In accordance with STDP, synaptic weight increases if the postsynaptic neuron generates a pulse (spike) immediately after the presynaptic one, and vice versa, the synaptic weight decreases if the postsynaptic neuron generates a spike right before the presynaptic one. Moreover, the smaller the time difference Δt between the pre- and postsynaptic spikes, the more pronounced the weight change will be.

According to one of the researchers, Head of the UNN PTRI laboratory Alexei Mikhailov, in order to demonstrate the STDP principle, memristive nanostructures based on yttria-stabilized zirconia (YSZ) thin films were used. YSZ is a well-known solid-state electrolyte with high oxygen ion mobility.

“Due to a specified concentration of oxygen vacancies, which is determined by the controlled concentration of yttrium impurities, and the heterogeneous structure of the films obtained by magnetron sputtering, such memristive structures demonstrate controlled bipolar switching between different resistive states in a wide resistance range. The switching is associated with the formation and destruction of conductive channels along grain boundaries in the polycrystalline ZrO2 (Y) film,” notes Alexei Mikhailov.

An array of memristive devices for research was implemented in the form of a microchip mounted in a standard cermet casing, which facilitates the integration of the array into a neural network’s analog circuit. The full technological cycle for creating memristive microchips is currently implemented at the UNN PTRI. In the future, it is possible to scale the devices down to the minimum size of about 50 nm, as was established by Greek partners.
Our studies of the dynamic plasticity of the memoristive devices, continues Alexey Mikhailov, have shown that the form of the conductance change depending on Δt is in good agreement with the STDP learning rules. It should be also noted that if the initial value of the memristor conductance is close to the maximum, it is easy to reduce the corresponding weight while it is difficult to enhance it, and in the case of a memristor with a minimum conductance in the initial state, it is difficult to reduce its weight, but it is easy to enhance it.

According to Vyacheslav Demin, director-coordinator in the area of nature-like technologies of the Kurchatov Institute, who is one of the ideologues of this work, the established pattern of change in the memristor conductance clearly demonstrates the possibility of hardware implementation of the so-called local learning rules. Such rules for changing the strength of synaptic connections depend only on the values ​​of variables that are present locally at each time point (neuron activities and current weights).

“This essentially distinguishes such principle from the traditional learning algorithm, which is based on global rules for changing weights, using information on the error values ​​at the current time point for each neuron of the output neural network layer (in a widely popular group of error back propagation methods). The traditional principle is not biosimilar, it requires “external” (expert) knowledge of the correct answers for each example presented to the network (that is, they do not have the property of self-learning). This principle is difficult to implement on the basis of memristors, since it requires controlled precise changes of memristor conductances, as opposed to local rules. Such precise control is not always possible due to the natural variability (a wide range of parameters) of memristors as analog elements,” says Vyacheslav Demin.

Local learning rules of the STDP type implemented in hardware on memristors provide the basis for autonomous (“unsupervised”) learning of a spiking neural network. In this case, the final state of the network does not depend on its initial state, but depends only on the learning conditions (a specific sequence of pulses). According to Vyacheslav Demin, this opens up prospects for the application of local learning rules based on memristors when solving artificial intelligence problems with the use of complex spiking neural network architectures.

Here’s a link to and a citation for the paper,

Yttria-stabilized zirconia cross-point memristive devices for neuromorphic applications by A. V. Emelyanov, K. E. Nikiruy, A. Demin, V. V. Rylkov, A. I. Belov, D. S. Korolev, E. G. Gryaznov, D. A. Pavlov, O. N. Gorshkov, A. N. Mikhaylov, P. Dimitrakis. Microelectronic Engineering Volume 215, 15 July 2019, 110988 First available online 16 May 2019

This paper is behind a paywall.

Bad battery, good synapse from Stanford University

A May 4, 2019 news item on ScienceDaily announces the latest advance made by Stanford University and Sandia National Laboratories in the field of neuromorphic (brainlike) computing,

The brain’s capacity for simultaneously learning and memorizing large amounts of information while requiring little energy has inspired an entire field to pursue brain-like — or neuromorphic — computers. Researchers at Stanford University and Sandia National Laboratories previously developed one portion of such a computer: a device that acts as an artificial synapse, mimicking the way neurons communicate in the brain.

In a paper published online by the journal Science on April 25 [2019], the team reports that a prototype array of nine of these devices performed even better than expected in processing speed, energy efficiency, reproducibility and durability.

Looking forward, the team members want to combine their artificial synapse with traditional electronics, which they hope could be a step toward supporting artificially intelligent learning on small devices.

“If you have a memory system that can learn with the energy efficiency and speed that we’ve presented, then you can put that in a smartphone or laptop,” said Scott Keene, co-author of the paper and a graduate student in the lab of Alberto Salleo, professor of materials science and engineering at Stanford who is co-senior author. “That would open up access to the ability to train our own networks and solve problems locally on our own devices without relying on data transfer to do so.”

An April 25, 2019 Stanford University news release (also on EurekAlert but published May 3, 2019) by Taylor Kubota, which originated the news item, expands on the theme,

A bad battery, a good synapse

The team’s artificial synapse is similar to a battery, modified so that the researchers can dial up or down the flow of electricity between the two terminals. That flow of electricity emulates how learning is wired in the brain. This is an especially efficient design because data processing and memory storage happen in one action, rather than a more traditional computer system where the data is processed first and then later moved to storage.

Seeing how these devices perform in an array is a crucial step because it allows the researchers to program several artificial synapses simultaneously. This is far less time consuming than having to program each synapse one-by-one and is comparable to how the brain actually works.

In previous tests of an earlier version of this device, the researchers found their processing and memory action requires about one-tenth as much energy as a state-of-the-art computing system needs in order to carry out specific tasks. Still, the researchers worried that the sum of all these devices working together in larger arrays could risk drawing too much power. So, they retooled each device to conduct less electrical current – making them much worse batteries but making the array even more energy efficient.

The 3-by-3 array relied on a second type of device – developed by Joshua Yang at the University of Massachusetts, Amherst, who is co-author of the paper – that acts as a switch for programming synapses within the array.

“Wiring everything up took a lot of troubleshooting and a lot of wires. We had to ensure all of the array components were working in concert,” said Armantas Melianas, a postdoctoral scholar in the Salleo lab. “But when we saw everything light up, it was like a Christmas tree. That was the most exciting moment.”

During testing, the array outperformed the researchers’ expectations. It performed with such speed that the team predicts the next version of these devices will need to be tested with special high-speed electronics. After measuring high energy efficiency in the 3-by-3 array, the researchers ran computer simulations of a larger 1024-by-1024 synapse array and estimated that it could be powered by the same batteries currently used in smartphones or small drones. The researchers were also able to switch the devices over a billion times – another testament to its speed – without seeing any degradation in its behavior.

“It turns out that polymer devices, if you treat them well, can be as resilient as traditional counterparts made of silicon. That was maybe the most surprising aspect from my point of view,” Salleo said. “For me, it changes how I think about these polymer devices in terms of reliability and how we might be able to use them.”

Room for creativity

The researchers haven’t yet submitted their array to tests that determine how well it learns but that is something they plan to study. The team also wants to see how their device weathers different conditions – such as high temperatures – and to work on integrating it with electronics. There are also many fundamental questions left to answer that could help the researchers understand exactly why their device performs so well.

“We hope that more people will start working on this type of device because there are not many groups focusing on this particular architecture, but we think it’s very promising,” Melianas said. “There’s still a lot of room for improvement and creativity. We only barely touched the surface.”

Here’s a link to and a citation for the paper,

Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing by Elliot J. Fuller, Scott T. Keene, Armantas Melianas, Zhongrui Wang, Sapan Agarwal, Yiyang Li, Yaakov Tuchman, Conrad D. James, Matthew J. Marinella, J. Joshua Yang3, Alberto Salleo, A. Alec Talin1. Science 25 Apr 2019: eaaw5581 DOI: 10.1126/science.aaw5581

This paper is behind a paywall.

For anyone interested in more about brainlike/brain-like/neuromorphic computing/neuromorphic engineering/memristors, use any or all of those terms in this blog’s search engine.

Brainlike computing with spintronic devices

Adding to the body of ‘memristor’ research I have here, there’s an April 17, 2019 news item on Nanowerk announcing the development of ‘memristor’ hardware by Japanese researchers (Note: A link has been removed),

A research group from Tohoku University has developed spintronics devices which are promising for future energy-efficient and adoptive computing systems, as they behave like neurons and synapses in the human brain (Advanced Materials, “Artificial Neuron and Synapse Realized in an Antiferromagnet/Ferromagnet Heterostructure Using Dynamics of Spin–Orbit Torque Switching”).

Just because this ‘synapse’ is pretty,

Courtesy: Tohoku University

An April 16, 2019 Tohoku University press release, which originated the news item, expands on the theme,

Today’s information society is built on digital computers that have evolved drastically for half a century and are capable of executing complicated tasks reliably. The human brain, by contrast, operates under very limited power and is capable of executing complex tasks efficiently using an architecture that is vastly different from that of digital computers.

So the development of computing schemes or hardware inspired by the processing of information in the brain is of broad interest to scientists in fields ranging from physics, chemistry, material science and mathematics, to electronics and computer science.

In computing, there are various ways to implement the processing of information by a brain. Spiking neural network is a kind of implementation method which closely mimics the brain’s architecture and temporal information processing. Successful implementation of spiking neural network requires dedicated hardware with artificial neurons and synapses that are designed to exhibit the dynamics of biological neurons and synapses.

Here, the artificial neuron and synapse would ideally be made of the same material system and operated under the same working principle. However, this has been a challenging issue due to the fundamentally different nature of the neuron and synapse in biological neural networks.

The research group – which includes Professor Hideo Ohno (currently the university president), Associate Professor Shunsuke Fukami, Dr. Aleksandr Kurenkov and Professor Yoshihiko Horio – created an artificial neuron and synapse by using spintronics technology. Spintronics is an academic field that aims to simultaneously use an electron’s electric (charge) and magnetic (spin) properties.

The research group had previously developed a functional material system consisting of antiferromagnetic and ferromagnetic materials. This time, they prepared artificial neuronal and synaptic devices microfabricated from the material system, which demonstrated fundamental behavior of biological neuron and synapse – leaky integrate-and-fire and spike-timing-dependent plasticity, respectively – based on the same concept of spintronics.

The spiking neural network is known to be advantageous over today’s artificial intelligence for the processing and prediction of temporal information. Expansion of the developed technology to unit-circuit, block and system levels is expected to lead to computers that can process time-varying information such as voice and video with a small amount of power or edge devices that have the an ability to adopt users and the environment through usage.

Here’s a link to and a citation for the paper,

Artificial Neuron and Synapse Realized in an Antiferromagnet/Ferromagnet Heterostructure Using Dynamics of Spin–Orbit Torque Switching by Aleksandr Kurenkov, Samik DuttaGupta, Chaoliang Zhang, Shunsuke Fukami, Yoshihiko Horio, Hideo Ohno. Advanced Materials https://doi.org/10.1002/adma.201900636 First published: 16 April 2019

This paper is behind a paywall.

Mimicking the brain with an evolvable organic electrochemical transistor

Simone Fabiano and Jennifer Gerasimov have developed a learning transistor that mimics the way synapses function. Credit: Thor Balkhed

At a guess, this was originally a photograph which has been passed through some sort of programme to give it a paintinglike quality.

Moving onto the research, I don’t see any reference to memristors (another of the ‘devices’ that mimics the human brain) so perhaps this is an entirely different way to mimic human brains? A February 5, 2019 news item on ScienceDaily announces the work from Linkoping University (Sweden),

A new transistor based on organic materials has been developed by scientists at Linköping University. It has the ability to learn, and is equipped with both short-term and long-term memory. The work is a major step on the way to creating technology that mimics the human brain.

A February 5, 2019 Linkoping University press release (also on EurekAlert), which originated the news item, describes this ‘nonmemristor’ research into brainlike computing in more detail,

Until now, brains have been unique in being able to create connections where there were none before. In a scientific article in Advanced Science, researchers from Linköping University describe a transistor that can create a new connection between an input and an output. They have incorporated the transistor into an electronic circuit that learns how to link a certain stimulus with an output signal, in the same way that a dog learns that the sound of a food bowl being prepared means that dinner is on the way.

A normal transistor acts as a valve that amplifies or dampens the output signal, depending on the characteristics of the input signal. In the organic electrochemical transistor that the researchers have developed, the channel in the transistor consists of an electropolymerised conducting polymer. The channel can be formed, grown or shrunk, or completely eliminated during operation. It can also be trained to react to a certain stimulus, a certain input signal, such that the transistor channel becomes more conductive and the output signal larger.

“It is the first time that real time formation of new electronic components is shown in neuromorphic devices”, says Simone Fabiano, principal investigator in organic nanoelectronics at the Laboratory of Organic Electronics, Campus Norrköping.

The channel is grown by increasing the degree of polymerisation of the material in the transistor channel, thereby increasing the number of polymer chains that conduct the signal. Alternatively, the material may be overoxidised (by applying a high voltage) and the channel becomes inactive. Temporary changes of the conductivity can also be achieved by doping or dedoping the material.

“We have shown that we can induce both short-term and permanent changes to how the transistor processes information, which is vital if one wants to mimic the ways that brain cells communicate with each other”, says Jennifer Gerasimov, postdoc in organic nanoelectronics and one of the authors of the article.

By changing the input signal, the strength of the transistor response can be modulated across a wide range, and connections can be created where none previously existed. This gives the transistor a behaviour that is comparable with that of the synapse, or the communication interface between two brain cells.

It is also a major step towards machine learning using organic electronics. Software-based artificial neural networks are currently used in machine learning to achieve what is known as “deep learning”. Software requires that the signals are transmitted between a huge number of nodes to simulate a single synapse, which takes considerable computing power and thus consumes considerable energy.

“We have developed hardware that does the same thing, using a single electronic component”, says Jennifer Gerasimov.

“Our organic electrochemical transistor can therefore carry out the work of thousands of normal transistors with an energy consumption that approaches the energy consumed when a human brain transmits signals between two cells”, confirms Simone Fabiano.

The transistor channel has not been constructed using the most common polymer used in organic electronics, PEDOT, but instead using a polymer of a newly-developed monomer, ETE-S, produced by Roger Gabrielsson, who also works at the Laboratory of Organic Electronics and is one of the authors of the article. ETE-S has several unique properties that make it perfectly suited for this application – it forms sufficiently long polymer chains, is water-soluble while the polymer form is not, and it produces polymers with an intermediate level of doping. The polymer PETE-S is produced in its doped form with an intrinsic negative charge to balance the positive charge carriers (it is p-doped).

Here’s a link to and a citation for the paper,

An Evolvable Organic Electrochemical Transistor for Neuromorphic Applications by Jennifer Y. Gerasimov, Roger Gabrielsson, Robert Forchheimer, Eleni Stavrinidou, Daniel T. Simon, Magnus Berggren, Simone Fabiano. Advanced Science DOI: https://doi.org/10.1002/advs.201801339 First published: 04 February 2019

This paper is open access.

There’s one other image associated this work that I want to include here,

Synaptic transistor. Sketch of the organic electrochemical transistor, formed by electropolymerization of ETE‐S in the transistor channel. The electrolyte solution is confined by a PDMS well (not shown). In this work, we define the input at the gate as the presynaptic signal and the response at the drain as the postsynaptic terminal. During operation, the drain voltage is kept constant while the gate is pulsed. Synaptic weight is defined as the amplitude of the current response to a standard gate voltage characterization pulse of −0.1 V. Different memory functionalities are accessible by applying gate voltage Courtesy: Linkoping University Researchers

An artificial synapse tuned by light, a ferromagnetic memristor, and a transparent, flexible artificial synapse

Down the memristor rabbit hole one more time.* I started out with news about two new papers and inadvertently found two more. In a bid to keep this posting to a manageable size, I’m stopping at four.

UK

In a June 19, 2019 Nanowerk Spotlight article, Dr. Neil Kemp discusses memristors and some of his latest work (Note: A link has been removed),

Memristor (or memory resistors) devices are non-volatile electronic memory devices that were first theorized by Leon Chua in the 1970’s. However, it was some thirty years later that the first practical device was fabricated. This was in 2008 when a group led by Stanley Williams at HP Research Labs realized that switching of the resistance between a conducting and less conducting state in metal-oxide thin-film devices was showing Leon Chua’s memristor behaviour.

The high interest in memristor devices also stems from the fact that these devices emulate the memory and learning properties of biological synapses. i.e. the electrical resistance value of the device is dependent on the history of the current flowing through it.

There is a huge effort underway to use memristor devices in neuromorphic computing applications and it is now reasonable to imagine the development of a new generation of artificial intelligent devices with very low power consumption (non-volatile), ultra-fast performance and high-density integration.

These discoveries come at an important juncture in microelectronics, since there is increasing disparity between computational needs of Big Data, Artificial Intelligence (A.I.) and the Internet of Things (IoT), and the capabilities of existing computers. The increases in speed, efficiency and performance of computer technology cannot continue in the same manner as it has done since the 1960s.

To date, most memristor research has focussed on the electronic switching properties of the device. However, for many applications it is useful to have an additional handle (or degree of freedom) on the device to control its resistive state. For example memory and processing in the brain also involves numerous chemical and bio-chemical reactions that control the brain structure and its evolution through development.

To emulate this in a simple solid-state system composed of just switches alone is not possible. In our research, we are interested in using light to mediate this essential control.

We have demonstrated that light can be used to make short and long-term memory and we have shown how light can modulate a special type of learning, called spike timing dependent plasticity (STDP). STDP involves two neuronal spikes incident across a synapse at the same time. Depending on the relative timing of the spikes and their overlap across the synaptic cleft, the connection strength is other strengthened or weakened.

In our earlier work, we were only able to achieve to small switching effects in memristors using light. In our latest work (Advanced Electronic Materials, “Percolation Threshold Enables Optical Resistive-Memory Switching and Light-Tuneable Synaptic Learning in Segregated Nanocomposites”), we take advantage of a percolating-like nanoparticle morphology to vastly increase the magnitude of the switching between electronic resistance states when light is incident on the device.

We have used an inhomogeneous percolating network consisting of metallic nanoparticles distributed in filamentary-like conduction paths. Electronic conduction and the resistance of the device is very sensitive to any disruption of the conduction path(s).

By embedding the nanoparticles in a polymer that can expand or contract with light the conduction pathways are broken or re-connected causing very large changes in the electrical resistance and memristance of the device.

Our devices could lead to the development of new memristor-based artificial intelligence systems that are adaptive and reconfigurable using a combination of optical and electronic signalling. Furthermore, they have the potential for the development of very fast optical cameras for artificial intelligence recognition systems.

Our work provides a nice proof-of-concept but the materials used means the optical switching is slow. The materials are also not well suited to industry fabrication. In our on-going work we are addressing these switching speed issues whilst also focussing on industry compatible materials.

Currently we are working on a new type of optical memristor device that should give us orders of magnitude improvement in the optical switching speeds whilst also retaining a large difference between the resistance on and off states. We hope to be able to achieve nanosecond switching speeds. The materials used are also compatible with industry standard methods of fabrication.

The new devices should also have applications in optical communications, interfacing and photonic computing. We are currently looking for commercial investors to help fund the research on these devices so that we can bring the device specifications to a level of commercial interest.

If you’re interested in memristors, Kemp’s article is well written and quite informative for nonexperts, assuming of course you can tolerate not understanding everything perfectly.

Here are links and citations for two papers. The first is the latest referred to in the article, a May 2019 paper and the second is a paper appearing in July 2019.

Percolation Threshold Enables Optical Resistive‐Memory Switching and Light‐Tuneable Synaptic Learning in Segregated Nanocomposites by Ayoub H. Jaafar, Mary O’Neill, Stephen M. Kelly, Emanuele Verrelli, Neil T. Kemp. Advanced Electronic Materials DOI: https://doi.org/10.1002/aelm.201900197 First published: 28 May 2019

Wavelength dependent light tunable resistive switching graphene oxide nonvolatile memory devices by Ayoub H.Jaafar, N.T.Kemp. DOI: https://doi.org/10.1016/j.carbon.2019.07.007 Carbon Available online 3 July 2019

The first paper (May 2019) is definitely behind a paywall and the second paper (July 2019) appears to be behind a paywall.

Dr. Kemp’s work has been featured here previously in a January 3, 2018 posting in the subsection titled, Shining a light on the memristor.

China

This work from China was announced in a June 20, 2019 news item on Nanowerk,

Memristors, demonstrated by solid-state devices with continuously tunable resistance, have emerged as a new paradigm for self-adaptive networks that require synapse-like functions. Spin-based memristors offer advantages over other types of memristors because of their significant endurance and high energy effciency.

However, it remains a challenge to build dense and functional spintronic memristors with structures and materials that are compatible with existing ferromagnetic devices. Ta/CoFeB/MgO heterostructures are commonly used in interfacial PMA-based [perpendicular magnetic anisotropy] magnetic tunnel junctions, which exhibit large tunnel magnetoresistance and are implemented in commercial MRAM [magnetic random access memory] products.

“To achieve the memristive function, DW is driven back and forth in a continuous manner in the CoFeB layer by applying in-plane positive or negative current pulses along the Ta layer, utilizing SOT that the current exerts on the CoFeB magnetization,” said Shuai Zhang, a coauthor in the paper. “Slowly propagating domain wall generates a creep in the detection area of the device, which yields a broad range of intermediate resistive states in the AHE [anomalous Hall effect] measurements. Consequently, AHE resistance is modulated in an analog manner, being controlled by the pulsed current characteristics including amplitude, duration, and repetition number.”

“For a follow-up study, we are working on more neuromorphic operations, such as spike-timing-dependent plasticity and paired pulsed facilitation,” concludes You. …

Here’s are links to and citations for the paper (Note: It’s a little confusing but I believe that one of the links will take you to the online version, as for the ‘open access’ link, keep reading),

A Spin–Orbit‐Torque Memristive Device by Shuai Zhang, Shijiang Luo, Nuo Xu, Qiming Zou, Min Song, Jijun Yun, Qiang Luo, Zhe Guo, Ruofan Li, Weicheng Tian, Xin Li, Hengan Zhou, Huiming Chen, Yue Zhang, Xiaofei Yang, Wanjun Jiang, Ka Shen, Jeongmin Hong, Zhe Yuan, Li Xi, Ke Xia, Sayeef Salahuddin, Bernard Dieny, Long You. Advanced Electronic Materials Volume 5, Issue 4 April 2019 (print version) 1800782 DOI: https://doi.org/10.1002/aelm.201800782 First published [online]: 30 January 2019 Note: there is another DOI, https://doi.org/10.1002/aelm.201970022 where you can have open access to Memristors: A Spin–Orbit‐Torque Memristive Device (Adv. Electron. Mater. 4/2019)

The paper published online in January 2019 is behind a paywall and the paper (almost the same title) published in April 2019 has a new DOI and is open access. Final note: I tried accessing the ‘free’ paper and opened up a free file for the artwork featuring the work from China on the back cover of the April 2019 of Advanced Electronic Materials.

Korea

Usually when I see the words transparency and flexibility, I expect to see graphene is one of the materials. That’s not the case for this paper (link to and citation for),

Transparent and flexible photonic artificial synapse with piezo-phototronic modulator: Versatile memory capability and higher order learning algorithm by Mohit Kumar, Joondong Kim, Ching-Ping Wong. Nano Energy Volume 63, September 2019, 103843 DOI: https://doi.org/10.1016/j.nanoen.2019.06.039 Available online 22 June 2019

Here’s the abstract for the paper where you’ll see that the material is made up of zinc oxide silver nanowires,

An artificial photonic synapse having tunable manifold synaptic response can be an essential step forward for the advancement of novel neuromorphic computing. In this work, we reported the development of highly transparent and flexible two-terminal ZnO/Ag-nanowires/PET photonic artificial synapse [emphasis mine]. The device shows purely photo-triggered all essential synaptic functions such as transition from short-to long-term plasticity, paired-pulse facilitation, and spike-timing-dependent plasticity, including in the versatile memory capability. Importantly, strain-induced piezo-phototronic effect within ZnO provides an additional degree of regulation to modulate all of the synaptic functions in multi-levels. The observed effect is quantitatively explained as a dynamic of photo-induced electron-hole trapping/detraining via the defect states such as oxygen vacancies. We revealed that the synaptic functions can be consolidated and converted by applied strain, which is not previously applied any of the reported synaptic devices. This study will open a new avenue to the scientific community to control and design highly transparent wearable neuromorphic computing.

This paper is behind a paywall.

Artificial synapse courtesy of nanowires

It looks like a popsicle to me,

Caption: Image captured by an electron microscope of a single nanowire memristor (highlighted in colour to distinguish it from other nanowires in the background image). Blue: silver electrode, orange: nanowire, yellow: platinum electrode. Blue bubbles are dispersed over the nanowire. They are made up of silver ions and form a bridge between the electrodes which increases the resistance. Credit: Forschungszentrum Jülich

Not a popsicle but a representation of a device (memristor) scientists claim mimics a biological nerve cell according to a December 5, 2018 news item on ScienceDaily,

Scientists from Jülich [Germany] together with colleagues from Aachen [Germany] and Turin [Italy] have produced a memristive element made from nanowires that functions in much the same way as a biological nerve cell. The component is able to both save and process information, as well as receive numerous signals in parallel. The resistive switching cell made from oxide crystal nanowires is thus proving to be the ideal candidate for use in building bioinspired “neuromorphic” processors, able to take over the diverse functions of biological synapses and neurons.

A Dec. 5, 2018 Forschungszentrum Jülich press release (also on EurekAlert), which originated the news item, provides more details,

Computers have learned a lot in recent years. Thanks to rapid progress in artificial intelligence they are now able to drive cars, translate texts, defeat world champions at chess, and much more besides. In doing so, one of the greatest challenges lies in the attempt to artificially reproduce the signal processing in the human brain. In neural networks, data are stored and processed to a high degree in parallel. Traditional computers on the other hand rapidly work through tasks in succession and clearly distinguish between the storing and processing of information. As a rule, neural networks can only be simulated in a very cumbersome and inefficient way using conventional hardware.

Systems with neuromorphic chips that imitate the way the human brain works offer significant advantages. Experts in the field describe this type of bioinspired computer as being able to work in a decentralised way, having at its disposal a multitude of processors, which, like neurons in the brain, are connected to each other by networks. If a processor breaks down, another can take over its function. What is more, just like in the brain, where practice leads to improved signal transfer, a bioinspired processor should have the capacity to learn.

“With today’s semiconductor technology, these functions are to some extent already achievable. These systems are however suitable for particular applications and require a lot of space and energy,” says Dr. Ilia Valov from Forschungszentrum Jülich. “Our nanowire devices made from zinc oxide crystals can inherently process and even store information, as well as being extremely small and energy efficient,” explains the researcher from Jülich’s Peter Grünberg Institute.

For years memristive cells have been ascribed the best chances of being capable of taking over the function of neurons and synapses in bioinspired computers. They alter their electrical resistance depending on the intensity and direction of the electric current flowing through them. In contrast to conventional transistors, their last resistance value remains intact even when the electric current is switched off. Memristors are thus fundamentally capable of learning.

In order to create these properties, scientists at Forschungszentrum Jülich and RWTH Aachen University used a single zinc oxide nanowire, produced by their colleagues from the polytechnic university in Turin. Measuring approximately one ten-thousandth of a millimeter in size, this type of nanowire is over a thousand times thinner than a human hair. The resulting memristive component not only takes up a tiny amount of space, but also is able to switch much faster than flash memory.

Nanowires offer promising novel physical properties compared to other solids and are used among other things in the development of new types of solar cells, sensors, batteries and computer chips. Their manufacture is comparatively simple. Nanowires result from the evaporation deposition of specified materials onto a suitable substrate, where they practically grow of their own accord.

In order to create a functioning cell, both ends of the nanowire must be attached to suitable metals, in this case platinum and silver. The metals function as electrodes, and in addition, release ions triggered by an appropriate electric current. The metal ions are able to spread over the surface of the wire and build a bridge to alter its conductivity.

Components made from single nanowires are, however, still too isolated to be of practical use in chips. Consequently, the next step being planned by the Jülich and Turin researchers is to produce and study a memristive element, composed of a larger, relatively easy to generate group of several hundred nanowires offering more exciting functionalities.

The Italians have also written about the work in a December 4, 2018 news item for the Polytecnico di Torino’s inhouse magazine, PoliFlash’. I like the image they’ve used better as it offers a bit more detail and looks less like a popsicle. First, the image,

Courtesy: Polytecnico di Torino

Now, the news item, which includes some historical information about the memristor (Note: There is some repetition and links have been removed),

Emulating and understanding the human brain is one of the most important challenges for modern technology: on the one hand, the ability to artificially reproduce the processing of brain signals is one of the cornerstones for the development of artificial intelligence, while on the other the understanding of the cognitive processes at the base of the human mind is still far away.

And the research published in the prestigious journal Nature Communications by Gianluca Milano and Carlo Ricciardi, PhD student and professor, respectively, of the Applied Science and Technology Department of the Politecnico di Torino, represents a step forward in these directions. In fact, the study entitled “Self-limited single nanowire systems combining all-in-one memristive and neuromorphic functionalities” shows how it is possible to artificially emulate the activity of synapses, i.e. the connections between neurons that regulate the learning processes in our brain, in a single “nanowire” with a diameter thousands of times smaller than that of a hair.

It is a crystalline nanowire that takes the “memristor”, the electronic device able to artificially reproduce the functions of biological synapses, to a more performing level. Thanks to the use of nanotechnologies, which allow the manipulation of matter at the atomic level, it was for the first time possible to combine into one single device the synaptic functions that were individually emulated through specific devices. For this reason, the nanowire allows an extreme miniaturisation of the “memristor”, significantly reducing the complexity and energy consumption of the electronic circuits necessary for the implementation of learning algorithms.

Starting from the theorisation of the “memristor” in 1971 by Prof. Leon Chua – now visiting professor at the Politecnico di Torino, who was conferred an honorary degree by the University in 2015 – this new technology will not only allow smaller and more performing devices to be created for the implementation of increasingly “intelligent” computers, but is also a significant step forward for the emulation and understanding of the functioning of the brain.

“The nanowire memristor – said Carlo Ricciardirepresents a model system for the study of physical and electrochemical phenomena that govern biological synapses at the nanoscale. The work is the result of the collaboration between our research team and the RWTH University of Aachen in Germany, supported by INRiM, the National Institute of Metrological Research, and IIT, the Italian Institute of Technology.”

h.t for the Italian info. to Nanowerk’s Dec. 10, 2018 news item.

Here’s a link to and a citation for the paper,

Self-limited single nanowire systems combining all-in-one memristive and neuromorphic functionalities by Gianluca Milano, Michael Luebben, Zheng Ma, Rafal Dunin-Borkowski, Luca Boarino, Candido F. Pirri, Rainer Waser, Carlo Ricciardi, & Ilia Valov. Nature Communicationsvolume 9, Article number: 5151 (2018) DOI: https://doi.org/10.1038/s41467-018-07330-7 Published: 04 December 2018

This paper is open access.

Just use the search term “memristor” in the blog search engine if you’re curious about the multitudinous number of postings on the topic here.

Artificial synapse based on tantalum oxide from Korean researchers

This memristor story comes from South Korea as we progress on the way to neuromorphic computing (brainlike computing). A Sept. 7, 2018 news item on ScienceDaily makes the announcement,

A research team led by Director Myoung-Jae Lee from the Intelligent Devices and Systems Research Group at DGIST (Daegu Gyeongbuk Institute of Science and Technology) has succeeded in developing an artificial synaptic device that mimics the function of the nerve cells (neurons) and synapses that are response for memory in human brains. [sic]

Synapses are where axons and dendrites meet so that neurons in the human brain can send and receive nerve signals; there are known to be hundreds of trillions of synapses in the human brain.

This chemical synapse information transfer system, which transfers information from the brain, can handle high-level parallel arithmetic with very little energy, so research on artificial synaptic devices, which mimic the biological function of a synapse, is under way worldwide.

Dr. Lee’s research team, through joint research with teams led by Professor Gyeong-Su Park from Seoul National University; Professor Sung Kyu Park from Chung-ang University; and Professor Hyunsang Hwang from Pohang University of Science and Technology (POSTEC), developed a high-reliability artificial synaptic device with multiple values by structuring tantalum oxide — a trans-metallic material — into two layers of Ta2O5-x and TaO2-x and by controlling its surface.

A September 7, 2018 DGIST press release (also on EurekAlert), which originated the news item, delves further into the work,

The artificial synaptic device developed by the research team is an electrical synaptic device that simulates the function of synapses in the brain as the resistance of the tantalum oxide layer gradually increases or decreases depending on the strength of the electric signals. It has succeeded in overcoming durability limitations of current devices by allowing current control only on one layer of Ta2O5-x.

In addition, the research team successfully implemented an experiment that realized synapse plasticity [or synaptic plasticity], which is the process of creating, storing, and deleting memories, such as long-term strengthening of memory and long-term suppression of memory deleting by adjusting the strength of the synapse connection between neurons.

The non-volatile multiple-value data storage method applied by the research team has the technological advantage of having a small area of an artificial synaptic device system, reducing circuit connection complexity, and reducing power consumption by more than one-thousandth compared to data storage methods based on digital signals using 0 and 1 such as volatile CMOS (Complementary Metal Oxide Semiconductor).

The high-reliability artificial synaptic device developed by the research team can be used in ultra-low-power devices or circuits for processing massive amounts of big data due to its capability of low-power parallel arithmetic. It is expected to be applied to next-generation intelligent semiconductor device technologies such as development of artificial intelligence (AI) including machine learning and deep learning and brain-mimicking semiconductors.

Dr. Lee said, “This research secured the reliability of existing artificial synaptic devices and improved the areas pointed out as disadvantages. We expect to contribute to the development of AI based on the neuromorphic system that mimics the human brain by creating a circuit that imitates the function of neurons.”

Here’s a link to and a citation for the paper,

Reliable Multivalued Conductance States in TaOx Memristors through Oxygen Plasma-Assisted Electrode Deposition with in Situ-Biased Conductance State Transmission Electron Microscopy Analysis by Myoung-Jae Lee, Gyeong-Su Park, David H. Seo, Sung Min Kwon, Hyeon-Jun Lee, June-Seo Kim, MinKyung Jung, Chun-Yeol You, Hyangsook Lee, Hee-Goo Kim, Su-Been Pang, Sunae Seo, Hyunsang Hwang, and Sung Kyu Park. ACS Appl. Mater. Interfaces, 2018, 10 (35), pp 29757–29765 DOI: 10.1021/acsami.8b09046 Publication Date (Web): July 23, 2018

Copyright © 2018 American Chemical Society

This paper is open access.

You can find other memristor and neuromorphic computing stories here by using the search terms I’ve highlighted,  My latest (more or less) is an April 19, 2018 posting titled, New path to viable memristor/neuristor?

Finally, here’s an image from the Korean researchers that accompanied their work,

Caption: Representation of neurons and synapses in the human brain. The magnified synapse represents the portion mimicked using solid-state devices. Credit: Daegu Gyeongbuk Institute of Science and Technology(DGIST)

Bringing memristors to the masses and cutting down on energy use

One of my earliest posts featuring memristors (May 9, 2008) focused on their potential for energy savings but since then most of my postings feature research into their application in the field of neuromorphic (brainlike) computing. (For a description and abbreviated history of the memristor go to this page on my Nanotech Mysteries Wiki.)

In a sense this July 30, 2018 news item on Nanowerk is a return to the beginning,

A new way of arranging advanced computer components called memristors on a chip could enable them to be used for general computing, which could cut energy consumption by a factor of 100.

This would improve performance in low power environments such as smartphones or make for more efficient supercomputers, says a University of Michigan researcher.

“Historically, the semiconductor industry has improved performance by making devices faster. But although the processors and memories are very fast, they can’t be efficient because they have to wait for data to come in and out,” said Wei Lu, U-M professor of electrical and computer engineering and co-founder of memristor startup Crossbar Inc.

Memristors might be the answer. Named as a portmanteau of memory and resistor, they can be programmed to have different resistance states–meaning they store information as resistance levels. These circuit elements enable memory and processing in the same device, cutting out the data transfer bottleneck experienced by conventional computers in which the memory is separate from the processor.

A July 30, 2018 University of Michigan news release (also on EurekAlert), which originated the news item, expands on the theme,

… unlike ordinary bits, which are 1 or 0, memristors can have resistances that are on a continuum. Some applications, such as computing that mimics the brain (neuromorphic), take advantage of the analog nature of memristors. But for ordinary computing, trying to differentiate among small variations in the current passing through a memristor device is not precise enough for numerical calculations.

Lu and his colleagues got around this problem by digitizing the current outputs—defining current ranges as specific bit values (i.e., 0 or 1). The team was also able to map large mathematical problems into smaller blocks within the array, improving the efficiency and flexibility of the system.

Computers with these new blocks, which the researchers call “memory-processing units,” could be particularly useful for implementing machine learning and artificial intelligence algorithms. They are also well suited to tasks that are based on matrix operations, such as simulations used for weather prediction. The simplest mathematical matrices, akin to tables with rows and columns of numbers, can map directly onto the grid of memristors.

The memristor array situated on a circuit board.

The memristor array situated on a circuit board. Credit: Mohammed Zidan, Nanoelectronics group, University of Michigan.

Once the memristors are set to represent the numbers, operations that multiply and sum the rows and columns can be taken care of simultaneously, with a set of voltage pulses along the rows. The current measured at the end of each column contains the answers. A typical processor, in contrast, would have to read the value from each cell of the matrix, perform multiplication, and then sum up each column in series.

“We get the multiplication and addition in one step. It’s taken care of through physical laws. We don’t need to manually multiply and sum in a processor,” Lu said.

His team chose to solve partial differential equations as a test for a 32×32 memristor array—which Lu imagines as just one block of a future system. These equations, including those behind weather forecasting, underpin many problems science and engineering but are very challenging to solve. The difficulty comes from the complicated forms and multiple variables needed to model physical phenomena.

When solving partial differential equations exactly is impossible, solving them approximately can require supercomputers. These problems often involve very large matrices of data, so the memory-processor communication bottleneck is neatly solved with a memristor array. The equations Lu’s team used in their demonstration simulated a plasma reactor, such as those used for integrated circuit fabrication.

This work is described in a study, “A general memristor-based partial differential equation solver,” published in the journal Nature Electronics.

It was supported by the Defense Advanced Research Projects Agency (DARPA) (grant no. HR0011-17-2-0018) and by the National Science Foundation (NSF) (grant no. CCF-1617315).

Here’s a link and a citation for the paper,

A general memristor-based partial differential equation solver by Mohammed A. Zidan, YeonJoo Jeong, Jihang Lee, Bing Chen, Shuo Huang, Mark J. Kushner & Wei D. Lu. Nature Electronicsvolume 1, pages411–420 (2018) DOI: https://doi.org/10.1038/s41928-018-0100-6 Published: 13 July 2018

This paper is behind a paywall.

For the curious, Dr. Lu’s startup company, Crossbar can be found here.