Agentic Symbolic Search: Approximating Solutions of PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks
Read the original on arXiv Machine Learning →Agentic Symbolic Search (ASYS) is a method that uses coding agents to build and refine explicit approximations of nonlinear partial differential equations (PDEs) by combining evolutionary search over differentiable symbolic programs with gradient-based fitting. ASYS evaluates candidate expressions using the governing PDE, guiding revisions toward more accurate representations. In applied tests, ASYS successfully inferred missing decay terms for a singular Constantin-Lax-Majda profile, reduced error in Fujita blow-up dynamics from 55.5% to 0.0879%, and produced a 14‑parameter mode‑coupling law for Allen‑Cahn interfaces that matches independent simulations.
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