Computers designed to work more like the human brain are proving capable of solving complex mathematical problems that were once considered the domain of powerful supercomputers.
Researchers at Sandia National Laboratories have developed a new algorithm that allows neuromorphic computers to solve partial differential equations, or PDEs. These equations are central to many scientific and engineering simulations, including weather forecasting, fluid motion, electromagnetic fields, structural mechanics, and nuclear physics.
The study, published in Nature Machine Intelligence, shows that brain-inspired hardware can handle these demanding calculations efficiently, using a very different approach from conventional computers.
Taking on Supercomputer-Level Mathematics
Partial differential equations are among the most important tools in modern science. They help researchers model how physical systems change over space and time. However, solving them usually requires large amounts of computing power, which is why they are often handled by advanced supercomputers.
Neuromorphic computers process information in a way inspired by the brainโs networks of neurons. Until recently, they were mostly associated with tasks such as pattern recognition, machine learning, and artificial intelligence. Many experts did not expect them to be useful for strict mathematical problems like PDEs.
Sandia researchers Brad Theilman and Brad Aimone have now shown that this assumption may be wrong. Their algorithm enables neuromorphic hardware to solve sparse finite element problems, a class of mathematical problems widely used in simulations of real-world physics.
The breakthrough suggests that brain-like computing could become a powerful new tool for scientific computation.
Why the Brain Is a Powerful Model
The researchers argue that the human brain already performs extremely complex calculations every day. Actions such as catching a ball, walking, balancing, or reacting quickly to movement require rapid and sophisticated processing.
While ordinary digital computers need large amounts of energy to solve certain problems, the brain performs many complex tasks with remarkable efficiency. Neuromorphic systems aim to capture some of that efficiency by using brain-like circuits and methods of computation.
According to the researchers, this study shows that real physics problems can be solved using brain-inspired computation, challenging the belief that only traditional supercomputers are suited for such tasks.
Toward Low-Energy Supercomputers
The discovery could have major implications for energy-efficient computing. Modern supercomputers consume enormous amounts of electricity, especially when running large simulations for science, engineering, and national security.
Neuromorphic hardware may offer a way to perform some of these calculations with far less power. This could be especially important for organizations that rely heavily on simulation, including the National Nuclear Security Administration, which uses supercomputers to model complex physical systems.
If neuromorphic systems continue to improve, they could eventually help create a new generation of low-energy supercomputers.
A New Link Between Neuroscience and Mathematics
The research may also offer new insights into how the brain itself performs computations. The Sandia team based its circuit on a known model from computational neuroscience and found that it has an unexpected connection to partial differential equations.
This connection could help scientists better understand the relationship between brain function, mathematics, and computation.
The researchers suggest that some brain disorders may eventually be understood as problems in computation. If scientists can better explain how the brain processes information, neuromorphic computing may one day contribute to research on neurological conditions such as Alzheimerโs disease and Parkinsonโs disease.
A Step Toward the Future of Computing
Neuromorphic computing is still developing, but this work marks an important advance. It shows that brain-inspired machines may be useful not only for artificial intelligence but also for solving serious scientific and engineering problems.
By bringing together neuroscience, mathematics, and computer engineering, researchers may be opening a new path toward faster, smarter, and more energy-efficient computing systems.
Journal Reference:
Theilman, B. H., & Aimone, J. B. (2025). Solving sparse finite element problems on neuromorphic hardware. Nature Machine Intelligence, 7(11), 1845. https://doi.org/10.1038/s42256-025-01143-2