{"ID":2894225,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.00855","arxiv_id":"2508.00855","title":"A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks","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 MSE reductions of up to three orders of magnitude compared to baseline methods. This work bridges the gap between deep learning and physics-driven modeling, offering a robust solution for multiscale and time-dependent PDE systems.","short_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 Re...","url_abs":"https://arxiv.org/abs/2508.00855","url_pdf":"https://arxiv.org/pdf/2508.00855v2","authors":"[\"Ziyang Zhang\",\"Feifan Zhang\",\"Weidong Tang\",\"Lei Shi\",\"Tailai Chen\"]","published":"2025-07-15T03:45:42Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\",\"physics.flu-dyn\"]","methods":"[\"Transformer\",\"Generative Adversarial Network\"]","has_code":false}