NeuroPINNs: Neuroscience Inspired Physics Informed Neural Networks

TL;DR

NeuroPINNs integrate biologically inspired spiking neuron models into physics-informed neural networks to enable energy-efficient PDE solving suitable for neuromorphic hardware, overcoming challenges of discontinuous dynamics with a novel stochastic projection method.

Contribution

This work introduces NeuroPINNs, a novel neural network framework that incorporates spiking neuron models into PINNs, enhancing energy efficiency and compatibility with neuromorphic hardware for PDE solving.

Findings

Achieved high accuracy on multiple PDE problems.

Significantly reduced communication and energy consumption.

Demonstrated effectiveness in 3D linear elastic micromechanics.

Abstract

We introduce NeuroPINNs, a neuroscience-inspired extension of Physics-Informed Neural Networks (PINNs) that incorporates biologically motivated spiking neuron models to achieve energy-efficient PDE solving. Unlike conventional PINNs, which rely on continuously firing activations and therefore incur high computational and energy costs, NeuroPINNs leverage Variable Spiking Neurons (VSNs) to enable sparse, event-driven communication. This makes them particularly well-suited for deployment on neuromorphic hardware and for scenarios with constrained computational resources, such as embedded and edge devices. A central challenge, however, lies in reconciling the discontinuous dynamics of spiking neurons with the smooth residual-based loss formulation required in PINNs. Direct smoothing introduces systematic biases, leading to inaccurate PDE learning. To overcome this, we employ a novel stochastic projection method inspired from upscaled theory that faithfully captures spiking behavior while maintaining compatibility with gradient-based optimization. Standard surrogate backpropagation is used for parameter updates, ensuring computational tractability. We demonstrate the effectiveness of NeuroPINNs on four representative PDE problems across both regular and irregular domains. Furthermore, application of NeuroPINN for linear elastic micromechnics in three dimensions was also explored. Results show that NeuroPINNs achieve high accuracy while substantially reducing communication and energy demands, marking a step toward scalable, neuromorphic-ready scientific machine learning.