arXiv AI

OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference

arXiv AI

Jul 14

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.

By Pengfei Cai, Utkarsh Utkarsh, Alan Edelman, Christopher Vincent Rackauckas, Rafael Gomez-Bombarelli

llms reinforcement-learning benchmarks

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.

By Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas, Venkataramana Runkana

agents benchmarks

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.

By Jaehyeon Park, Mingu Kang, Dongseok Lee, Woojin Cho, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park

llms

Hugging Face Trending Papers

Oct 9

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.

llms

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.

By Han Wan, Rui Zhang, Hao Sun

llms benchmarks

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:...

By Langchen Liu, Junlin Luo, Min Zhu, Zhuoran Yang, Lu Lu

llms fine-tuning benchmarks

arXiv Machine Learning

Jun 18

Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.

By Kuilin Qin, Lianfang Wang, Xu Sun, Jiwei Jia, Yu Wang, Yong Wang, Yuping Duan

arXiv Machine Learning

Oct 2

Geometry-physics confounding impairs PDE learning across varying domains

arXiv:2609.38623v1 Announce Type: new Abstract: Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing...

By Yinghao Cheng, Gengxiang Chen, Xu Liu, Qinglu Meng, Yixin Jing, Xiangguo Tang, Wenping Mou, Lihui Wang, Yingguang Li

benchmarks

arXiv Machine Learning

Jul 28

Physics Transformer: Tailoring Transformer for General PDE Prediction

arXiv:2607. 24513v1 Announce Type: new Abstract: Transformer architectures have attracted increasing attention for solving partial differential equations (PDEs), owing to their flexibility in handling irregular discretizations and their ability to capture long-range physical dependencies.

By Guoze Sun, Rui Zhang, Jiankai Tang, Mengtao Yan, Runze Mao, Zhi X. Chen, Hao Sun

llms nlp benchmarks

arXiv AI

Jul 10

LLT: Local Linear Transformer for PDE Operator Learning

arXiv:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.

By Oded Ovadia, Eli Turkel

llms safety

arXiv Machine Learning

Jul 14

LLM-PDESR: Robust PDE Discovery via Subdomain Weighted Residuals and LLM-Guided Symbolic Hypothesis Generation

arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.

By Jinyang Du, Hao Ma, Xiaohu Shi, Bo Yang, Yanchun Liang, Heow Pueh Lee, Chunguo Wu

llms benchmarks

arXiv AI

Jun 6

Semantic Partial Grounding via LLMs

arXiv:2602. 22067v2 Announce Type: replace Abstract: Grounding is a critical step in classical planning, yet it often becomes a computational bottleneck due to the exponential growth in grounded actions and atoms as task size increases.

By Giuseppe Canonaco, Alberto Pozanco, Daniel Borrajo

llms rag benchmarks

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