The paper introduces GAV, a scientific experimentation environment that generates verifiable PDE problems by learning a distribution of reference solutions and using the method of manufactured solutions to construct matching PDEs. GAV includes a Generator, Agent, and Verifier that together enable iterative program improvement and provide numerical feedback on accuracy and computational cost. Experiments on Navier–Stokes and Vlasov–Poisson equations show that GAV can significantly reduce test errors for existing PDE agents.
arXiv:2606. 10752v1 Announce Type: new Abstract: Numerical solvers for partial differential equations (PDEs) are core computational tools in science and engineering.
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: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.
The paper investigates whether AI agents can reliably generate complete, executable JSON specifications for automated PDE simulation, covering geometry creation, meshing, solving, and result export. Using a workflow that combines model extraction, deterministic scientific checks, clarification, and validated local patches, the authors evaluate specification correctness, execution completion, and numerical verification across 120 template-related requests. The approach achieves 98.3% correct first-turn specifications, outperforms schema-assisted and model-only baselines, and demonstrates successful automated execution in 30 complex 3D cases and 75% success in live user-to-results tests.
The paper introduces Re4, a scientific computing agent that employs a four-step logical chain—rewriting, resolution, review, and revision—using three large language models: a Consultant, a Programmer, and a Reviewer. The Consultant rewrites problem descriptions by linking them to domain knowledge, the Programmer generates and runs code, and the Reviewer iteratively refines the code through self-debugging. Experiments on PDEs, fluid dynamics, ill‑conditioned linear systems, and data‑driven physics show that this collaborative framework markedly improves bug‑free code generation and execution success rates across several LLMs.
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE 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.
arXiv:2608. 04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem.
arXiv:2610.08720v1 Announce Type: new Abstract: LLM-based agents are increasingly advancing scientific and engineering problem solving, with physics simulation emerging as a challenging yet practical...
arXiv:2606. 09774v1 Announce Type: new Abstract: Advanced scientific simulators expose specialized input languages that turn simulation goals into executable configurations, but learning them can cost domain scientists hours to days.