arXiv AI
OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference
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Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards
arXiv:2607. 10474v1 Announce Type: cross Abstract: Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments.
arXiv AI
Jul 7
PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
arXiv:2607. 05134v1 Announce Type: cross Abstract: We present PDEFlow, an autonomous agentic framework that turns user-level ODE and PDE descriptions into solver-backed neural-operator pipelines.
arXiv Machine Learning
Oct 12
PDE-PFN: Prior-Data Fitted Neural PDE Solver
PDE-PFN is a prior‑data fitted neural solver that uses in‑context learning to approximate the posterior predictive mean of partial differential equation (PDE) solutions. It builds on a Transformer‑based PFN architecture with self‑ and cross‑attention, and is pre‑trained on noisy approximate solutions generated by physics‑informed neural networks. Experiments on various two‑dimensional PDEs show that PDE‑PFN generalizes across heterogeneous equations, remains robust to noisy priors, and can perform zero‑gradient‑update inference while achieving competitive or better predictive accuracy compared to baselines.
Hugging Face Trending Papers
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PDE-PFN: Prior-Data Fitted Neural PDE Solver
PDE-PFN is a prior-data fitted neural solver that uses in-context learning to approximate the posterior predictive mean of partial differential equation (PDE) solutions. It builds on a Transformer-based PFN architecture with self- and cross-attention, and is pre‑trained on noisy approximate solutions generated by physics‑informed neural networks. Experiments on various two‑dimensional PDEs show that PDE‑PFN generalizes across heterogeneous equations, remains robust to noisy priors, and can perform zero‑gradient‑update inference while achieving competitive or improved predictive accuracy compared to baselines.
arXiv AI
Aug 5
Large language models for partial differential equation workflows
arXiv:2608. 03600v1 Announce Type: new Abstract: Partial differential equations (PDEs) become actionable in science and engineering not as isolated formulae, but as executable workflows that connect modelling assumptions, governing equations, numerical solvers, diagnostics, and decisions.
arXiv AI
Oct 21
FoundPDE: A generative foundation model for data-driven symbolic discovery of partial differential equations
arXiv:2610.26963v1 Announce Type: cross Abstract: Discovering governing partial differential equations (PDEs) from observed data is a central inverse problem in computational science and engineering:...