[2508.00855] A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks

Computer Science > Machine Learning arXiv:2508.00855 (cs) [Submitted on 15 Jul 2025 (v1), last revised 2 Apr 2026 (this version, v2)] Title:A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks Authors:Ziyang Zhang, Feifan Zhang, Weidong Tang, Lei Shi, Tailai Chen View a PDF of the paper titled A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks, by Ziyang Zhang and 4 other authors View PDF Abstract:Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and violations of temporal causality. To address these limitations, we propose a novel Residual Guided Training strategy for Physics-Informed Transformer via Generative Adversarial Networks (GAN). Our framework integrates a decoder-only Transformer to inherently capture temporal correlations through autoregressive processing, coupled with a residual-aware GAN that dynamically identifies and prioritizes high-residual regions. By introducing a causal penalty term and an adaptive sampling mechanism, the method enforces temporal causality while refining accuracy in problematic domains. Extensive numerical experiments on the Allen-Cahn, Klein-Gordon, and Navier-Stokes equations demonstrate significant improvements, achieving relative MS...