让用户用自然语言写方程，自动完成求解、训练和预测。
PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
- 用自然语言描述方程，自动生成可执行的物理问题规范。
- 基于有限元求解器生成数据，训练出可泛化的神经算子模型。
- 适合需要反复配置、仿真、学习物理系统的科研与工程场景。
我们提出PDEFlow，一个自主代理框架，可将用户提供的常微分方程（ODE）和偏微分方程（PDE）描述自动转化为基于求解器的神经算子流程。该工作流涵盖问题定义、数据生成、算子训练与基于检查点的推理。状态化输入图将多轮自然语言输入与用户修改转换为验证后的有效问题规范。数据生成模块采样参数，使用FEniCSx有限元后端求解控制方程，并将结果存储为算子可用张量。训练与推理阶段采用注册表式接口，支持不同神经算子在不改变整体流程的前提下训练与部署。当前实现中，采用多分支贝叶斯DeepONet。在基准ODE与PDE任务上的实验表明，PDEFlow能构建有效规范、生成求解器支持的数据集、训练跨稳态与瞬态问题类别的神经算子，并从保存的检查点提供无需求解器的预测。该框架旨在实现可重复的科学与工程工作流，适用于需大量相似物理配置的建模、仿真、学习与查询任务。
原文摘要 · Abstract (English)
We present PDEFlow, an autonomous agentic framework that turns user-level ODE and PDE descriptions into solver-backed neural-operator pipelines. The workflow links problem specification, data generation, operator training, and checkpoint-based inference. A stateful input graph converts multi-turn natural-language input and user edits into validated problem specifications. The data-generation module then samples parameters, solves the configured governing-equation with FEniCSx finite-element backend, and stores the solutions as operator-ready tensors. The training and inference stages use a registry-based interface, allowing different neural operators to be trained and deployed without changing the surrounding pipeline. In the current implementation, we instantiate this interface with a multi-branch Bayesian DeepONet. Experiments on benchmark ODE and PDE tasks show that PDEFlow can construct valid specifications, generate solver-backed datasets, train neural operators across steady and transient problem classes, and provide solver-free predictions from saved checkpoints. The framework is designed for repeatable scientific and engineering workflows where many related physics configurations must be specified, simulated, learned, and queried with minimal manual intervention.
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