ASYS让AI自动去发现偏微分方程的数学结构，比如给Allen-Cahn和Keller-Segel找到了以前没人写出来的公式。搞数学或数值计算的可以看看。
ASYS（Agentic Symbolic Search）是一个结合进化搜索与梯度优化的智能体框架，用于自动发现偏微分方程的符号表示。在Allen-Cahn 2D问题中，它生成了几何界面公式；在Keller-Segel趋化模型中，它找到了九参数收缩律。该框架不依赖手工推导、网格数值解或神经网络逼近，在五个案例中均产出了可解释的数学结构。ASYS实现了符号回归之外的归纳偏差注入，为理解PDE解提供了新范式。
Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks
Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structures directly. We propose Agentic Symbolic Search (ASYS), a prior-guided framework in which an agent translates PDE theory, public problem constraints, and accumulated search experience into testable differentiable symbolic programs. The mathematical forms are refined under evolutionary search, while their continuous parameters are fit by gradient-based optimization. This makes the search an automated form of inductive-bias injection rather than blind symbolic regression. For problems with known analytical forms, ASYS recovers these forms naturally; for other problems, ASYS constructs analytical approximations which can guide mathematicians toward further analysis. In our experiments, across five problems spanning bounded dynamics, finite-time blow-up, and free-boundary focusing, ASYS produces interpretable representations, including a geometric interface formula for Allen-Cahn 2D dynamics and a nine-parameter contraction law for Keller-Segel chemotactic blow-up, in settings where no closed-form description was previously available. ASYS shows the possibility of a new paradigm for characterizing PDE solutions, beyond handcrafted analytical solutions, mesh-based numerical solutions, and neural network approximations.