Simulation is central to modern engineering and science, but the cost of numerical solvers for partial differential equations (PDEs) remains a bottleneck whenever fast or many-query evaluations are re...
arXiv:2608.24547v1 Announce Type: new Abstract: Simulation is central to modern engineering and science, but the cost of numerical solvers for partial differential equations (PDEs) remains a bottlene...
arXiv:2610.17221v1 Announce Type: cross Abstract: Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scali...
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
arXiv:2608.30328v1 Announce Type: new Abstract: Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditio...
arXiv:2602. 06842v2 Announce Type: replace-cross Abstract: Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence.
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
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.
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
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:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.