🔥 本文被 ICLR 2026 Workshop on AI with Recursive Self-Improvement 录用为 Spotlight！

🔥 This paper has been accepted as Spotlight at the ICLR 2026 Workshop on AI with Recursive Self-Improvement!

论文链接 / Paper: arXiv:2510.05158

作者 / Authors: Xin He, Liangliang You, Hongduan Tian, Bo Han, Ivor Tsang, Yew-Soon Ong

中文版

研究动机

物理信息神经网络（Physics-Informed Neural Networks, PINNs）是求解偏微分方程（PDEs）的强大工具，但传统构建流程繁琐且易出错：

科学家需要手动将实际问题转化为 PDE 形式
需要精心设计网络架构和损失函数
需要实现稳定的训练流程

这一过程对专业知识要求极高，限制了 PINNs 的广泛应用。

核心方法

Lang-PINN 提出了一个 LLM 驱动的多智能体系统，能够从自然语言任务描述自动构建可执行的 PINN 求解器。系统由四个协作智能体组成：

1. PDE Agent（PDE 智能体）

解析自然语言任务描述，提取偏微分方程中的算子、系数以及边界/初始条件，将其转化为符号化的 PDE 表示。

2. PINN Agent（PINN 智能体）

根据 PDE 的特征（周期性、几何复杂度、多尺度动态等），自动选择合适的神经网络架构和归纳偏置。

3. Code Agent（代码智能体）

生成模块化的、可执行的 PINN 训练代码实现。

4. Feedback Agent（反馈智能体）

执行代码，诊断错误，并向前面的阶段提供迭代式的修正反馈，确保最终输出的科学有效性。

实验结果

误差降低：均方误差（MSE）降低了 3-5 个数量级
执行成功率：端到端执行成功率提升超过 50%
计算效率：时间开销减少高达 74%
可靠性：在 1D 和 2D 场景下成功率超过 80%，而基线方法通常低于 35%

English Version

Motivation

Physics-Informed Neural Networks (PINNs) are powerful tools for solving partial differential equations (PDEs), but the traditional workflow for constructing PINNs is labor-intensive and error-prone:

Scientists must manually formulate real-world problems as PDEs
Careful design of network architectures and loss functions is required
Implementing stable training pipelines demands deep domain expertise

These barriers significantly limit the broader adoption of PINNs.

Key Methods

Lang-PINN introduces an LLM-driven multi-agent system that automatically constructs executable PINN solvers from natural language task descriptions. The system consists of four collaborative agents:

1. PDE Agent

Parses natural language task descriptions to extract PDE operators, coefficients, and boundary/initial conditions, transforming them into symbolic PDE representations.

2. PINN Agent

Automatically selects appropriate neural network architectures and inductive biases based on PDE characteristics (periodicity, geometric complexity, multiscale dynamics, etc.).

3. Code Agent

Generates modular, executable PINN training code.

4. Feedback Agent

Executes the generated code, diagnoses errors, and provides iterative corrections to earlier stages, ensuring scientifically valid outputs.

Results

Error reduction: MSE reduced by 3–5 orders of magnitude
Execution success: End-to-end success rate improved by over 50%
Computational efficiency: Time overhead reduced by up to 74%
Reliability: Success rates exceed 80% in 1D and 2D regimes, vs. below 35% for baselines