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.
By Muhammad M. Akmal, Kamy Sepehrnoori, Michael J. Pyrcz
arXiv:2409. 08958v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability.
By Aleksander Krasowski, Jonas R. Naujoks, Moritz Weckbecker, Galip \"U. Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, Ren\'e P. Klausen
arXiv:2607. 10200v1 Announce Type: new Abstract: The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime.
By Bangti Jin, Longjun Wu
The paper introduces PAM-GS, a physics-aware gradient surgery technique for Physics-Informed Neural Networks (PINNs). It addresses the highly imbalanced multi-task optimisation problem in PINNs by adaptively mitigating task interference based on observed gradient conflicts. Experiments on four PDE benchmarks show that PAM-GS achieves competitive solution accuracy while maintaining strong task-balanced performance, outperforming existing methods on most problems.
By Thomas Borsani, Giuseppe Di Fatta
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.
By Chutian Huang, Chang Ma, Kaibo Wang, Yang Xiang
arXiv:2509. 01235v2 Announce Type: replace Abstract: Balancing training accuracy and adversarial robustness has beeen a challenge since the birth of deep learning.
By Yixiong Ren, Wenkang Du, Jianhui Zhou, Haiping Huang
EmbeddGAN introduces a new GAN framework that replaces the traditional discriminator with an embedding network trained to maximize statistical dependence between embeddings and real/fake labels using Gini distance correlation (gCor). The generator simultaneously minimizes this dependence, encouraging real and generated samples to become indistinguishable in the learned low‑dimensional embedding space. Experiments on MNIST, CIFAR‑10, and CelebA show competitive performance and notably more stable training dynamics compared to established baselines.
By MaTais Caldwell, Yixin Chen, Xin Dang, Charles Walter
arXiv:2602. 02547v2 Announce Type: replace-cross Abstract: Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data.
By Hankyeol Kim, Pilsung Kang
arXiv:2608. 12535v1 Announce Type: new Abstract: Deep learning models are widely used for time series analysis in domains such as healthcare, finance, energy systems, and environmental monitoring.
By Michael Baronov, Denis Vorobev, Margarita Rusanova, Petr Sokerin, Alexey Zaytsev
arXiv:2510. 18989v2 Announce Type: replace Abstract: Neural operators are commonly utilized as fast surrogates for numerical solvers in PDE problems, mapping input functions to solution functions.
By Yifei Sun
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.
By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
arXiv:2509. 24935v3 Announce Type: replace-cross Abstract: Scalability has driven recent advances in generative modeling, yet its principles remain underexplored for adversarial learning.
By Sangeek Hyun, MinKyu Lee, Jae-Pil Heo