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The paper evaluates whether LLM agents can reliably construct complete executable JSON specifications for automated PDE simulation setup (geometry, meshing, solving, export), showing a full workflow with scientific checks and clarification achieves 98.3% correct specification outcomes versus 92.5% schema-assisted single-shot and 82.5% model-only baselines.
This paper proposes HERO (History-Enriched Rollout Training), a method that augments standard trajectory supervision for autoregressive neural operators with relative supervision from the model's own optimization history, improving long-horizon accuracy and stability on PDE benchmarks.
Proposes semigroup consistency as a diagnostic for evaluating learned physics simulators, showing that normalized semigroup error correlates with rollout degradation in heat and Burgers dynamics using ConvNet and FNO baselines.