Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models

Abstract

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering.

References in corpus (15)

• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
• Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training
• Deep splitting method for parabolic PDEs
• Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism
• An Accelerated LIF Neuronal Network Array for a Large Scale Mixed-Signal Neuromorphic Architecture
• A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture
• Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equation
• Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions
• Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs)
• Physics-driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks
• PIAT: Physics Informed Adversarial Training for Solving Partial Differential Equations

Cited by in corpus (1)

• Surrogate Modeling of Landau Damping with Deep Operator Networks