The paper introduces a new type of data‑poisoning attack called a wrong‑physics backdoor, which tricks neural PDE operators into selecting a solution from the same PDE family but with an incorrect physical parameter. By relinking a surrogate input’s supervision to a cached alternate‑parameter solution, the attack keeps the output physically plausible yet wrong for the intended parameter. Experiments on 476 campaigns across several PDEs and models (FNO, DeepONet, Transformer, GRU, LSTM) show high success rates while maintaining low clean error, revealing a validation gap in current practices.
By Hanbing Liang, Fujun Liu
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
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: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).
By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar
arXiv:2609.24947v1 Announce Type: new
Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
By S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami
arXiv:2503.19081v2 Announce Type: replace
Abstract: Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PD...
By Serge Kotchourko, Amin Totounferoush, Michael W. Mahoney, Steffen Staab
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis
The paper introduces Fast Preemptive Robustification (FPR), a lightweight defense that enhances the robustness of deep neural networks against transferable adversarial attacks. By sharpening Laplacian responses through a single 3×3 channel‑wise convolution, FPR eliminates the need for surrogate models, iterative optimization, or specialized training. Experiments show that FPR lowers untargeted attack success rates by 12.7% and reduces targeted attack success from 10.7% to 4.1%.
By Jiaming Liang, Chi-Man Pun
arXiv:2606. 04420v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses.
By Anna Lazareva, Alexander Tarakanov
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:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation.