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

Fuente: arXiv
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Main Authors: Shekarpaz, Simin, Zeng, Fanhai, Karniadakis, George
Format: Preprint
Published: 2023
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author Shekarpaz, Simin
Zeng, Fanhai
Karniadakis, George
author_facet Shekarpaz, Simin
Zeng, Fanhai
Karniadakis, George
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_13205
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models
Shekarpaz, Simin
Zeng, Fanhai
Karniadakis, George
Numerical Analysis
Machine Learning
Neural and Evolutionary Computing
Computational Physics
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.
title Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models
topic Numerical Analysis
Machine Learning
Neural and Evolutionary Computing
Computational Physics
url https://arxiv.org/abs/2304.13205