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Volume 35, Issue 1
Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

Simin Shekarpaz, Fanhai Zeng & George Karniadakis

DOI: 10.4208/cicp.OA-2023-0121

Commun. Comput. Phys., 35 (2024), pp. 1-37.

Published online: 2024-01

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  • 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.

  • Keywords

Operator splitting, neuron models, fractional calculus.

  • AMS Subject Headings

92B20, 34C28, 37M05, 34A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-1, author = {Shekarpaz , SiminZeng , Fanhai and Karniadakis , George}, title = {Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {1}, pages = {1--37}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0121}, url = {http://global-sci.org/intro/article_detail/cicp/22894.html} }
TY - JOUR T1 - Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models AU - Shekarpaz , Simin AU - Zeng , Fanhai AU - Karniadakis , George JO - Communications in Computational Physics VL - 1 SP - 1 EP - 37 PY - 2024 DA - 2024/01 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0121 UR - https://global-sci.org/intro/article_detail/cicp/22894.html KW - Operator splitting, neuron models, fractional calculus. AB -

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.

Simin Shekarpaz, Fanhai Zeng & George Karniadakis. (2024). Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models. Communications in Computational Physics. 35 (1). 1-37. doi:10.4208/cicp.OA-2023-0121
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