EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks EvoPINN：面向物理信息神经网络的代理可执行算法发现

TL;DR

• EvoPINN is an agentic framework that automates the design of Physics-Informed Neural Networks (PINNs) by reformulating development into an execution-grounded algorithm discovery problem.
• It decouples neural representations from training programs and uses an LLM agent to iteratively propose memory-conditioned programmatic modifications, ensuring scientific validity through strict structural verification and budget-matched PDE evaluation.
• EvoPINN discovers PDE-specialized learning algorithms that significantly reduce relative $L_2$ error across diverse PDE regimes (oscillatory, elliptic, dissipative, nonlinear transport).
• It autonomously invents SLRC-PINN, a novel architecture whose performance gains persist under rigorous parameter-matched comparisons, demonstrating the viability of execution-grounded agents for discovering new scientific computing mechanisms.

Why It Matters

This work addresses a critical bottleneck in PINN development: the reliance on manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics. By leveraging LLM-based agentic frameworks with execution grounding, EvoPINN offers a scalable, automated approach to discover high-performing, scientifically valid PINN architectures, potentially accelerating advancements in solving complex partial differential equations across scientific and engineering domains.

Technical Details

• Modular Search Space: EvoPINN decouples neural representations from training programs, enabling independent exploration of architectural components and optimization strategies.
• LLM Agent with Memory Conditioning: An LLM agent proposes iterative programmatic modifications conditioned on past successful designs, facilitating guided search within the modular space.
• Strict Structural Verification: All candidate algorithms undergo validation to ensure mathematical correctness and numerical stability before evaluation.
• Budget-Matched PDE Evaluation: Candidates are assessed based on their ability to solve PDEs within fixed computational budgets, ensuring fair comparison and practical relevance.
• Diverse PDE Regimes: Experiments cover oscillatory, elliptic, dissipative, and nonlinear transport PDEs, demonstrating generalizability across different physical phenomena.
• SLRC-PINN Invention: EvoPINN autonomously develops SLRC-PINN, a novel architecture that outperforms baselines while maintaining comparable parameter counts, highlighting its capacity for genuine innovation.

Industry Insight

The success of EvoPINN underscores the potential of execution-grounded AI agents to automate and enhance scientific computing workflows, particularly in fields like physics-informed machine learning where domain-specific constraints are paramount. This approach could be extended to other areas requiring rigorous algorithmic discovery, such as quantum chemistry or climate modeling, reducing human effort and accelerating breakthroughs. Additionally, it sets a precedent for integrating LLMs with formal verification methods to ensure reliability in automated scientific tool development.

TL;DR

• EvoPINN 提出了一种基于智能体的框架，用于自动发现物理信息神经网络（PINN）的可执行算法。
• 该框架通过解耦神经网络表示与训练程序，利用大语言模型（LLM）代理迭代生成内存条件化的程序修改方案。
• 所有候选算法均经过严格结构验证和预算匹配的 PDE 评估，确保科学有效性。
• 实验表明 EvoPINN 在多种偏微分方程类型中显著降低相对 L₂ 误差，并自主发明了新型架构 SLRC-PINN。
• 研究证明了执行驱动型智能体在发现全新科学计算机制方面的可行性。

为什么值得看

本文解决了 PINN 开发中依赖人工试错的核心痛点，首次将算法设计转化为可执行的搜索问题，为自动化科学机器学习提供了新范式。其提出的“执行验证+内存引导”双约束机制有效避免了 LLM 生成无效代码的问题，对构建可靠 AI for Science 系统具有重要指导意义。

技术解析

• EvoPINN 将 PINN 构建过程分解为两个独立模块：神经网络结构与训练程序，允许 LLM 代理仅修改后者而保持前者稳定，从而降低搜索空间复杂度。
• 采用记忆-conditioned 的迭代优化策略，每次提案基于历史成功/失败记录进行调整，避免重复探索低效区域。
• 引入双重验证机制：语法层面的结构检查确保代码可运行，数值层面的 PDE 求解测试保证结果符合物理约束且误差可控。
• 在四类典型 PDE（振荡、椭圆、耗散、非线性输运）上进行基准测试，使用统一计算资源预算对比基线方法，突出泛化能力。
• 自主发明的 SLRC-PINN 架构包含自适应残差校正层与动态损失加权机制，经参数匹配后仍优于传统 PINN 及现有自动化方法。

行业启示

• 科学计算领域应转向“人机协同+执行验证”的 AI 研发模式，避免盲目信任纯文本生成的模型输出，需建立严格的沙箱测试流程。
• 未来 AutoML 工具应集成领域知识图谱与物理守恒律作为先验约束，提升生成结果的数学一致性与工程可用性。
• 研究机构可优先布局针对特定物理场景的专用智能体框架（如流体力学、量子系统等），而非追求通用型解决方案，以实现更快落地与更高精度。