More Subtly Dangerous than AI: The "Brain is Computing" Hypothesis Resonates in Engineering—Neuromorphic × Physical Simulation

The Common Belief that "Brain-like Computers Struggle with Math" is Shaken

Neuromorphic computers are machines inspired by the neural circuits of the brain. They can process information in parallel and asynchronously with ultra-low power consumption. However, it has long been thought that they are not suitable for "precise numerical calculations," especially partial differential equations (PDEs), which are central to physical simulations. On January 7, 2026, an article based on an announcement from Sandia National Laboratories was published on Phys.org, introducing research that challenges this assumption. It suggests that brain-like computers can solve PDEs surprisingly well. Phys.org

The main focus of the research is the "marriage" of the Finite Element Method (FEM) and Spiking Neural Networks (SNN). FEM is a classic method for obtaining approximate solutions by discretizing PDEs that describe phenomena such as fluid dynamics, electromagnetic fields, and structural mechanics into large (but sparse) systems of linear equations $Ax=b$. Modern science and technology, from weather forecasting to material design, cannot be discussed without FEM. News Releases

NeuroFEM: Translating Numerical Analysis Instead of "Learning" It

The study (published in Nature Machine Intelligence, open access) presents an algorithm called "NeuroFEM" that maps the structure of FEM's sparse matrix $A$ directly onto the connections of an SNN, converging to a solution through the timing of spikes. The key point is that it does not rely on "training the neural network to solve" the problem. Instead, it translates the already established mathematics of FEM into a form that is "native" to neuromorphic computing. Nature

According to the paper's summary, it demonstrated meaningful accuracy with the fundamental PDE known as the Poisson equation and "near-ideal scaling" on highly parallel neuromorphic hardware. The actual hardware used was Intel's research neuromorphic chip Loihi 2. It also showed potential for extension to other PDEs, such as linear elasticity, and to irregular 2D/3D meshes. Nature

Breaking Down the Mechanism: Each Mesh Node Becomes a "Small Neural Group"

In NeuroFEM, a group of about 8 to 16 neurons is assigned to each node of the FEM mesh (this is a hyperparameter). The non-zero elements of the sparse matrix $A$ are reflected as synaptic weights between nodes. The right-hand side $b$ is given as a bias added to each neuron, and noise input is also added to create an asynchronous balanced firing state. Since spike trains are not numerical values per se, a low-pass filter-like readout is used to reconstruct the estimated solution for each node. Nature

An interesting aspect is addressing the issue of "a steady bias remaining in the solution when directly mapped" by adding a state variable that integrates local residuals to each neuron, thus eliminating steady-state errors through distributed spiking PI (Proportional + Integral) control. This allows error correction using only local information without a "central command tower" overseeing the entire system. Nature

Furthermore, once the network is constructed, it can quickly adapt to different problems by merely changing the right-hand side (external forces or source terms) without requiring additional training. This suggests a use case where it continuously solves problems in response to sensor inputs in the field—a direction referred to as a "neuromorphic twin" in the paper. Nature

Why "Brain-like" Works for PDEs: The Argument of Power Efficiency and Scale

Sandia's news release points out that while PDEs are indispensable for modeling real-world phenomena like weather forecasting and material behavior, they have traditionally required enormous computational resources. It positions neuromorphic computing as potentially handling similar problems more power-efficiently by processing information like the brain. News Releases

The statements delve deeper. Mr. Theilman notes that while computational systems exhibiting intelligent-like behavior have emerged, they are "nothing like the brain and require (frankly) absurd resources." News Releases

Mr. Aimone also shares the intuition that motion control, like hitting a tennis ball, is a "very sophisticated computation" that the brain handles extremely cheaply. Phys.org

The key point here is that computations like PDE solvers are well-suited to "massive local computation," "sparse communication," and "asynchronous parallelism." Indeed, the paper states that the constraints of sparsity, distribution, and asynchrony inherent in the brain "oddly align" with the constraints faced by modern high-performance numerical computing, arguing that the sparse coupling derived from FEM can leverage the advantages of neuromorphic computing. Nature

However, It's Not a Panacea: The "Next Homework" on Accuracy, Implementation, and Evaluation

On the other hand, it is not yet promised as a "complete replacement for traditional supercomputers." The paper suggests that the absolute value of residuals can vary depending on settings and may be inferior to classical solvers (e.g., SciPy's spsolve), and that parameter selection can affect performance observations, prompting further investigation into numerical properties. Nature

Nevertheless, the fact that the "trustworthy mathematics" of FEM was transplanted without relying on black-box learning is significant. By bringing applied mathematics, computational neuroscience, and hardware design to the same table, there is potential for a new toolkit of "power-efficient simulations." Sandia also poses the next question: Is there a "neuromorphic version" that corresponds to more advanced applied mathematics methods? Phys.org

Summary of Reactions on SNS (as Confirmed in Public Scope)

※ Here, we organize the trends of reactions using only "posts and signals" that could actually be confirmed externally (we do not fabricate unverified X posts, etc.).

1. Researchers Emphasize the "Practical" Aspect (LinkedIn)
   In Mr. Aimone's LinkedIn post, he discusses how NeuroFEM can handle the "main workhorse" of sparse linear systems with low-power neuromorphic computing, its comparability as a numerical solver, the design philosophy that allows users to use it without "mastering SNN," and the brain-like sparsity, locality, and asynchrony derived from motor cortex models, with confirmed reactions (Likes). LinkedIn

2. "Immediate Response" to Code Release (GitHub)
   A repository for NeuroFEM has been released under the Sandia Labs name, with confirmed stars and forks. In the research community, whether there is an "entry point for reproducibility" can significantly influence the initial reception, making this a positive sign. GitHub

3. Picked Up by Curation-Type Newsletters (Medium)
   In an AI newsletter-style article, this research is listed as a paper published in Nature Machine Intelligence, creating a "path for visibility" to readers outside the field. Medium

4. Indicators of "Volume of Discussion": Altmetric and Share Counts
   The Nature page displays an Altmetric score (e.g., 67), indicating a certain level of online attention. Share counts are also displayed on the Phys.org side. Nature