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. 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:2609.24021v1 Announce Type: cross Abstract: Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying c...
The paper presents cross‑domain pretraining for neural surrogates in steady‑state computational fluid dynamics (CFD). By training models across varied geometries, boundary conditions, and fidelities, the authors show that such pretraining improves zero‑ and few‑shot performance compared to training from scratch or transferring from domain‑specific experts. Finetuning a pretrained cross‑domain model can reduce errors by 2–3× at the same sample size and require eight times fewer samples to reach the same error, with benefits that grow with model size and dataset diversity.
Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying coefficients, initial conditions, forcing terms, bou...
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...
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:2610.09255v1 Announce Type: new Abstract: Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors. Because s...
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
arXiv:2606. 15959v1 Announce Type: cross Abstract: Neural networks are used as generative surrogate models for scientific discovery, which are trainable approximations of scientific simulations.
arXiv:2605. 08843v2 Announce Type: replace Abstract: Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity.
The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.