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. Large language models (LLMs) are beginning to support such workflows by linking natural language, symbolic mathematics, code, solver outputs, and feedback. Here we examine recent advances in LLM-assisted PDE research across three stages: the discovery and formulation of governing models, the generation and revision of executable numerical solvers, and the use of simulation feedback to support control, design, and optimization. Across these stages, current systems act primarily as workflow-level interfaces. Despite this progress, the field remains limited by the scarcity of high-quality datasets and benchmarks, especially for knowledge discovery and real-world applications, where expert annotation, executable problem construction, and task-level feedback require substantial domain effort. A further challenge is the persistent gap between simulation-based results and real-world scientific and engineering systems, which limits the direct transfer of numerical simulations, control policies, and optimized designs to practical settings. These challenges make LLM-assisted PDE workflows a critical testbed for developing scientific AI systems that can connect language, computation, physical constraints, and real-world decision-making.
Sean R. Wilkinson, Valentine G. Anantharaj, Jong Youl Choi +8cs.AI cs.CE
Leadership computing facilities steward large-scale scientific datasets that routinely require substantial transformation before serving as AI training data. However, no existing framework fully unifies automated transformation, readiness assessment, provenance tracking, and agent-native deployment. We present REDI, an open-source framework that addresses this gap through a unified five-stage pipeline (ingest, preprocess, transform, structure, and output) with per-stage instrumentation for reproducibility and deployment as an agent-callable skill; companion tool SetGo automates FAIR compliance and catalog publication. Evaluated across climate, proteomics, materials science, and nuclear fusion, REDI transforms all datasets from raw to AI-ready, with outputs validated against domain-expert references, and preliminary results show near-ideal parallel scaling to 100 nodes on Frontier for the climate case. Provenance-instrumented profiling reveals file I/O as the dominant pipeline cost, with format selection a first-order optimization lever. These results establish REDI as a cross-domain platform providing automated data readiness for scientific AI, transforming data preparation bottlenecks into reproducible, reusable community assets.