NeuroPINNs: Neuroscience Inspired Physics Informed Neural Networks
Shailesh Garg, Souvik Chakraborty
TL;DR
NeuroPINNs address the high energy cost of traditional PINNs by embedding Variable Spiking Neurons to enable sparse, event-driven computation while enforcing PDE physics via a residual-based loss. Gradient evaluation for the PDE residual uses an upscale, stochastic projection (SP) method, with surrogate gradients used only for parameter updates, allowing native training of spiking networks. Across four representative PDEs on regular and irregular domains, as well as a 3D micromechanics application, NeuroPINNs achieve competitive accuracy with strong energy efficiency benefits and robust performance where conversion-based or vanilla SP-PINNs struggle. The work demonstrates the feasibility of neuromorphic-ready scientific ML for complex, high-dimensional PDEs and highlights directions for future improvements in SNN-specific training algorithms.
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.