AI 中文总结
该研究提出ADSL-PDE领域特定语言，通过结构化搜索空间提升神经PDE求解器自动设计的搜索效率与优化稳定性，前十次迭代性能提升超52%。
AI 中文摘要
神经偏微分方程（PDE）求解器的自动设计本质上是一个搜索空间表示问题。在无约束Python程序的空间中，有效求解器仅占极小一部分：大多数候选程序存在语法错误、语义不兼容或数值不稳定的问题。直接生成代码会迫使大语言模型（LLM）将大部分搜索能力用于处理实现失败，而非推理求解器的质量。ADSL-PDE通过在求解器概念与可执行代码之间引入结构化搜索状态来解决这一挑战，它表示决定神经PDE求解器的功能决策（包括架构、物理约束、目标、采样和优化），同时抽象掉底层实现细节。一个确定性编译器将每个有效的搜索状态映射为可执行求解器。实际上，ADSL-PDE重塑了搜索空间：它移除了大部分无效程序区域，提高了有意义候选的密度，同时保留了发现此前未见设计所需的组合自由度。因此，求解器进化可在设计决策而非代码制品上进行。基于此表示，我们的进化智能体利用经验反馈迭代地提出、评估和优化求解器搜索状态。在多个PDE基准测试中，ADSL-PDE同时提升了搜索效率和优化稳定性，在前十次进化迭代内实现了超过52%的性能提升。这些结果为LLM驱动的自动设计提供了更广泛的原则：有效的智能体不仅需要更强的推理能力，还需要能将探索集中在有效且重要决策上的搜索表示。
英文摘要
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 (architecture, physical constraints, objectives, sampling, and optimization) while abstracting away low-level implementation details. A deterministic compiler maps each valid search state to an executable solver. In effect, ADSL-PDE reshapes the search space: it removes large regions of invalid programs, increases the density of meaningful candidates, and preserves the compositional freedom needed to discover previously unseen designs. Solver evolution can thus operate over design decisions rather than code artifacts. Built on this representation, our evolutionary agent iteratively proposes, evaluates, and refines solver search states using empirical feedback. Across multiple PDE benchmarks, ADSL-PDE improves both search efficiency and optimization stability, achieving an improvement of more than 52% within the first ten evolution iterations. These results suggest a broader principle for LLM-driven auto-design: effective agents do not merely require stronger reasoning, but rather a search representation that concentrates exploration on valid and consequential decisions.
