arXiv:2510. 25731v2 Announce Type: replace-cross Abstract: Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering.
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arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
Gen-PINNs introduces a deterministic residual-adversarial framework that combines Generative Adversarial Networks with Physics-Informed Neural Networks to solve partial differential equations. The method addresses limitations of standard PINNs—such as spectral bias, loss imbalance, and optimizer stagnation—by using a generator that learns the PDE solution with dynamically weighted physics-informed losses and discriminators that assess residuals against zero-residual states. Experiments on nonlinear and higher-order PDEs (Burgers, Allen‑Cahn, Kuramoto‑Sivashinsky) show significant gains in accuracy and convergence, especially for sharp-front, stiff, and high-order problems.
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
The paper presents a theoretical framework for certifying the accuracy of physics‑informed neural networks (PINNs) used to solve partial differential equations. It derives generalization bounds that link the residual loss minimized during training to the actual error in the solution space, showing that if the neural approximation stays within a compact subset, a vanishing residual guarantees convergence to the true solution. Deterministic and probabilistic convergence results are provided, offering explicit error guarantees based on residual, boundary, and initial condition errors.
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.