ADSL-PDE: A Domain-Specific Language for Neural PDE Solver Auto-Design

A new arXiv paper (2608.04384) introduces ADSL-PDE, a domain-specific language designed to improve the auto-design of neural partial differential equation (PDE) solvers. The research addresses the challenge of representing the search space for neural PDE solvers, which are typically sparse and difficult for large language models (LLMs) to navigate. By introducing a structured search state that abstracts away low-level implementation details, ADSL-PDE allows LLMs to focus on solver quality rather than implementation failures. The language represents functional decisions such as architecture, physical constraints, objectives, sampling, and optimization, and a deterministic compiler maps valid search states to executable solvers. This approach reshapes the search space, removing invalid programs and improving efficiency. The paper is available on arXiv and represents a contribution to the intersection of AI and scientific computing.