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:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2605.15959v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral...
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.
arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
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:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv:2606. 25151v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing equations in their loss function, enabling mesh-free solutions to partial differential equations.
arXiv:2606. 02623v1 Announce Type: cross Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering.
The paper introduces StablePDENet, a physics-informed adversarial training framework that regularizes the residual sensitivity of neural operators to improve stability against input perturbations. The method formulates operator learning as a min–max optimization, where a physics-based projected‑gradient adversary generates perturbations and the outer objective combines the attacked physics loss with a normalized residual‑sensitivity penalty. Experiments on benchmark problems show that StablePDENet outperforms PI‑DeepONet and its adversarial variant in accuracy under adversarial attacks while maintaining competitive performance on clean data, and it also enhances generalization and highlights the distinction between model sensitivity and intrinsic operator ill‑conditioning.