A new algorithm lets neuromorphic hardware tackle the same mathematical problems used to model weather, electromagnetic fields, and nuclear weapons — using a fraction of the energy.
ALBUQUERQUE, N.M. — A computer chip designed to work like the human brain can now solve a class of mathematics problems that previously required a full-scale supercomputer, according to a study published in Nature Machine Intelligence by researchers at Sandia National Laboratories.
The chips, called neuromorphic processors, process information using networks of artificial neurons that fire electrical pulses — much like real brain cells do. Until now, most researchers assumed these chips were only useful for tasks like recognizing images or running artificial intelligence models. Solving rigorous mathematical equations was considered out of reach.
The new study shows that assumption was wrong.
What problem did they solve?
The researchers focused on a type of equation called a partial differential equation, or PDE. PDEs are the mathematical tools scientists use to describe how physical things change across space and time. They show up everywhere in engineering and science — in models of ocean currents, aircraft wing stress, electromagnetic signal propagation, and the physics of nuclear weapons.
Solving PDEs at a useful scale normally requires a supercomputer that consumes megawatts of electricity. The human brain, by comparison, runs on about 20 watts — roughly the same as a dim light bulb.
How does the new approach work?
Computational neuroscientists Brad Theilman and Brad Aimone developed an algorithm called NeuroFEM. It takes a standard engineering method for solving PDEs (called the finite element method) and translates it into a form that neuromorphic hardware can run using spiking neurons.
They tested it on Intel’s Oheo Gulch system, a machine built around 32 of Intel’s Loihi 2 neurochips. The hardware produced correct solutions, and it scaled efficiently: each time the number of processing cores was doubled, the time to solve the problem was cut roughly in half. That kind of scaling is difficult to achieve on conventional processors.
“We’re just starting to have computational systems that can exhibit intelligent-like behavior,” Theilman said in a statement released by Sandia National Laboratories. “But they look nothing like the brain, and the amount of resources that they require is ridiculous, frankly.”
Why does the brain connection matter?
The algorithm was not chosen at random. NeuroFEM closely mirrors the structure of cortical networks — the layers of neurons responsible for higher-order thinking in the mammalian brain. Theilman noted that this connection had gone unnoticed for more than a decade.
“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,” he said in the same statement.
Aimone pointed out that the brain is already solving problems of this complexity every time a person catches a ball or swings a bat. “These are very sophisticated computations,” he said in the statement. “They are exascale-level problems that our brains are capable of doing very cheaply.”
What are the practical applications?
The most immediate application is in national security. The research was funded in part by the National Nuclear Security Administration’s Advanced Simulation and Computing program, which runs the supercomputers used to simulate nuclear weapon physics without live testing. Those machines consume enormous amounts of power.
If neuromorphic chips can handle the same calculations at a much lower energy cost, it could significantly reduce the resources required to maintain the nuclear security enterprise.
The team also noted that NeuroFEM is designed to be easy to use. Engineers working on existing PDE problems would not need to rebuild their workflows from scratch to run them on neuromorphic hardware.
Sandia has described the work as a step toward the world’s first neuromorphic supercomputer.
What comes next?
The researchers plan to explore whether more advanced mathematical methods beyond the finite element method can also be translated into neuromorphic form. They also believe the work may have implications for medicine. If the brain is genuinely solving PDE-class problems during everyday movement and sensory processing, then diseases that damage those processes might one day be understood differently.
“Diseases of the brain could be diseases of computation,” Aimone said in the statement.
Sources
Theilman, B.H. and Aimone, J.B. (2025). “Solving sparse finite element problems on neuromorphic hardware.” Nature Machine Intelligence 7, 1845. https://www.nature.com/articles/s42256-025-01143-2
Quotes in this article are drawn from “Nature-inspired computers are shockingly good at math.” Sandia National Laboratories News Releases, January 7, 2026. https://newsreleases.sandia.gov/nature-inspired-computers-are-shockingly-good-at-math/
Ray Jackson holds a BSc in Electrical Engineering from the University of Manitoba and a PhD in Physics from Carleton University. His reporting interests include Current and Future Technologies, Engineering and Artificial Intelligence.