arXiv AI
When Does AI for PDEs Yield Scientific Evidence?
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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement
arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.
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Wrong-Physics Backdoors in Neural PDE Operators
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.
arXiv AI
Aug 25
One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs
arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...
arXiv Machine Learning
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ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv AI
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Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
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arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).