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.

翻译：非线性偏微分方程（PDEs）在建模复杂物理系统中至关重要，然而传统物理信息神经网络（PINNs）在关键时空区域中常面临残差未完全收敛以及时间因果性违反的挑战。为克服这些局限，我们提出一种基于生成对抗网络（GAN）的物理信息Transformer残差引导训练策略。该框架采用仅解码器Transformer，通过自回归处理天然捕捉时间相关性，并集成残差感知GAN动态识别与优先处理高残差区域。通过引入因果惩罚项与自适应采样机制，该方法在强制时间因果性的同时提升了问题区域的精度。基于Allen-Cahn、Klein-Gordon和Navier-Stokes方程的广泛数值实验表明，与基线方法相比，相对均方误差（MSE）最高降低三个数量级。本研究弥合了深度学习与物理驱动建模之间的鸿沟，为多尺度及时变PDE系统提供了稳健的解决方案。