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Performance Evaluation of High-Dimensional Spatio-Temporal Evolution Simulation Using Physics-Informed Neural Networks

Kosei WADA¹⁾, Makoto SASAKI¹⁾, Keisuke YANO²⁾

1)

Nihon University, Narashino 275-8575, Japan

2)

The Institute of Statistical Mathematics, Tachikawa 190-8562, Japan

(Received 1 May 2025 / Accepted 29 July 2025 / Published 15 October 2025)

Abstract

In this study, Physics-Informed Neural Networks (PINNs), a deep learning-based framework is applied to a partial differential equation in multi-dimensional space. As a preliminary investigation, the diffusion equation is solved and we examine how computation time varies with spatial dimensionality. The computational time with that of the Finite Difference Method (FDM) with keeping the computation accuracy. The results show that the PINNs can be faster than the FDM in a higher-dimensional space due to the mesh-free characteristics.

Copyright (c) 2025 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

physics-informed machine learning, PINNs, numerical simulation, plasma simulation, calculation accuracy

DOI: 10.1585/pfr.20.1203047

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