Brain inspired machines are better at math than expected

In a study published in Nature Machine Intelligence, Sandia National Laboratories computational neuroscientists Brad Theilman and Brad Aimone introduced a new algorithm that allows neuromorphic hardware to solve partial differential equations, or PDEs -- the mathematical foundation for modeling phenomena such as fluid dynamics, electromagnetic fields and structural mechanics.

The results demonstrate that neuromorphic systems can handle these equations efficiently. The advance could help open the door to the first neuromorphic supercomputer, offering a new path toward energy efficient computing for national security and other critical applications.

The research was funded by the Department of Energy's Office of Science through the Advanced Scientific Computing Research and Basic Energy Sciences programs, as well as the National Nuclear Security Administration's Advanced Simulation and Computing program.

Solving Partial Differential Equations With Brain Like Hardware

Partial differential equations are essential for simulating real world systems. They are used to forecast weather, analyze how materials respond to stress, and model complex physical processes. Traditionally, solving PDEs requires enormous computing power. Neuromorphic computers approach the problem differently by processing information in ways that resemble how the brain operates.

"We're just starting to have computational systems that can exhibit intelligent-like behavior. But they look nothing like the brain, and the amount of resources that they require is ridiculous, frankly," Theilman said.

For years, neuromorphic systems were mainly viewed as tools for pattern recognition or for speeding up artificial neural networks. Few expected them to manage mathematically rigorous problems such as PDEs, which are typically handled by large scale supercomputers.

Aimone and Theilman were not surprised by the outcome. They argue that the human brain routinely carries out highly complex calculations, even if people are unaware of it.

"Pick any sort of motor control task -- like hitting a tennis ball or swinging a bat at a baseball," Aimone said. "These are very sophisticated computations. They are exascale-level problems that our brains are capable of doing very cheaply."

Energy Efficient Computing for National Security

The findings could have major implications for the National Nuclear Security Administration, which is responsible for maintaining the nation's nuclear deterrent. Supercomputers used across the nuclear weapons complex consume vast amounts of electricity to simulate the physics of nuclear systems and other high stakes scenarios.

Neuromorphic computing may provide a way to significantly cut energy use while still delivering strong computational performance. By solving PDEs in a brain inspired manner, these systems suggest that large simulations could be run using far less power than conventional supercomputers require.

"You can solve real physics problems with brain-like computation," Aimone said. "That's something you wouldn't expect because people's intuition goes the opposite way. And in fact, that intuition is often wrong."

The team envisions neuromorphic supercomputers eventually becoming central to Sandia's mission of protecting national security.

What Neuromorphic Computing Reveals About the Brain

Beyond engineering advances, the research also touches on deeper questions about intelligence and how the brain performs calculations. The algorithm developed by Theilman and Aimone closely mirrors the structure and behavior of cortical networks.

"We based our circuit on a relatively well-known model in the computational neuroscience world," Theilman said. "We've shown the model has a natural but non-obvious link to PDEs, and that link hasn't been made until now -- 12 years after the model was introduced."

The researchers believe this work could help connect neuroscience with applied mathematics, offering new understanding of how the brain processes information.

"Diseases of the brain could be diseases of computation," Aimone said. "But we don't have a solid grasp on how the brain performs computations yet."

If that idea proves correct, neuromorphic computing might one day contribute to better understanding and treatment of neurological disorders such as Alzheimer's and Parkinson's.

Building the Next Generation of Supercomputers

Neuromorphic computing remains an emerging field, but this work represents an important step forward. The Sandia team hopes their results will encourage collaboration among mathematicians, neuroscientists and engineers to expand what this technology can achieve.

"If we've already shown that we can import this relatively basic but fundamental applied math algorithm into neuromorphic -- is there a corresponding neuromorphic formulation for even more advanced applied math techniques?" Theilman said.

As development continues, the researchers are optimistic. "We have a foot in the door for understanding the scientific questions, but also we have something that solves a real problem," Theilman said.