arXiv:2608. 15408v1 Announce Type: new Abstract: Deep operator networks can become statistically unstable when partial differential equation inputs are observed at thousands of strongly correlated sensors but only a small number of operator samples is available.
arXiv:2608.29069v1 Announce Type: cross Abstract: Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices...
arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.
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. 13629v1 Announce Type: cross Abstract: Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA).
arXiv:2608.21677v1 Announce Type: cross Abstract: Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route informat...
The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
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:2606. 28519v1 Announce Type: new Abstract: Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data.
arXiv:2512. 09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs).
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. 06827v1 Announce Type: new Abstract: Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear.
arXiv:2606. 11691v1 Announce Type: new Abstract: Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes.