Michigan Researchers Demonstrate Memristor-based PDE Solver

By Staff

August 1, 2018

Memristor technology is much discussed for many purposes, not least memory-based computing and reduced power consumption. Recently, a team of researchers implemented a partial differential equation solver fashioned from memristors, which they say may have broad applications spanning mobile computing to supercomputing. Their paper (A general memristor-based partial differential equation solver) appears the July 13, 20128 issue of Nature Electronics.

Led by Wei Lu, a professor of electrical and computer engineering at University of Michigan and co-founder of memristor startup Crossbar, the team reports developing a “complete memristor-based hardware and software system” able to perform high-precision computing tasks and reduce power consumption. The abstract does a nice job summarizing:

Memristor array on a circuit board. Photo credit: Mohammed Zidan, Nanoelectronics group, University of Michigan.

“Memristive devices have been extensively studied for data-intensive tasks such as artificial neural networks. These types of computing tasks are considered to be ‘soft’ as they can tolerate low computing precision without suffering from performance degradation. However, ‘hard’ computing tasks, which require high precision and accurate solutions, dominate many applications and are difficult to implement with memristors because the devices normally offer low native precision and suffer from high device variability.

“Here we report a complete memristor-based hardware and software system that can perform high-precision computing tasks, making memristor-based in-memory computing approaches attractive for general high-performance computing environments. We experimentally implement a numerical partial differential equation solver using a tantalum oxide memristor crossbar system, which we use to solve static and time-evolving problems. We also illustrate the practical capabilities of our memristive hardware by using it to simulate an argon plasma reactor.”

A brief account of the work is posted on the University of Michigan website. Unlike ordinary transistor-based 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.

As explained in the article, 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 “memory-processing units,” could be particularly useful for implementing machine learning and artificial intelligence algorithms say the researchers. 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.

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.

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.

Link to University of Michigan article: https://news.umich.edu/memory-processing-unit-could-bring-memristors-to-the-masses/

Link to Nature Electronics paper: https://www.nature.com/articles/s41928-018-0100-6

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