Improving Auto-Design of Neural PDE Solvers with a Domain-Specific Language

arXiv cs.AIAugust 6, 2026en

arXiv:2608.04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem. In the space of unrestricted Python programs, valid solvers form an extremely sparse subset: most candidate programs are syntactically incorrect, semantically incompatible, or numerically unstable. Direct code generation therefore forces an LLM to spend most of its search capacity navigating implementation failures rather than reasoning about solver quality. ADSL-PDE addresses this challenge by introducing a structured search state between solver concepts and executable code. It represents the functional decisions that determine a neural PDE solver (architectu

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