arXiv Machine Learning
Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
Hugging Face Trending Papers
Sep 21
Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver
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 AI
Jun 26
Error-Conditioned Neural Solvers
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.
Hugging Face Trending Papers
Aug 25
From Numerical Simulators of PDEs to Neural Emulators and Back
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 Machine Learning
Aug 26
From Numerical Simulators of PDEs to Neural Emulators and Back
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 Machine Learning
6d ago
Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers
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.
arXiv Machine Learning
Jun 17
Operator Boosting Produces Pareto-Efficient PDE Surrogates
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.