A Modular Framework with an Adaptive Momentum-based Evolutionary Strategy for Physics-Informed Neural Networks
提出一个模块化可扩展的进化策略框架MEES-PINN，用于解决物理信息神经网络在高维损失景观下的优化难题，并设计自适应动量自然进化策略AMNES，在多种偏微分方程基准测试中展现出更好的可扩展性和物理准确性。
Physics-Informed Neural Networks have emerged as a powerful tool for solving partial differential equations, but their success is often hindered by complex, high-dimensional loss landscapes. While evolutionary strategies offer a promising gradient-free alternative, standard methods struggle with the scalability required for modern deep learning models. In this article, we propose a Modular and Extensible Evolutionary-Strategy-based framework for Physics-Informed Neural Networks (MEES-PINN) that integrates problem-specific physics with evolutionary optimization. The framework is designed in a modular and flexible manner, enabling a seamless combination of different physical problems, neural architectures, and evolutionary algorithms within a single pipeline. It also provides a foundation to analyze PINN optimization through a “dual matching” requirement — aligning the network capacity with problem complexity and optimizer power with the network scale. To address the limitations of existing optimizers within this framework, we propose an Adaptive Momentum Natural Evolution Strategy (AMNES), which enhances xNES with an Adam-like scheme incorporating exponential moving averages (EMA) of first and second moments for the robust, scale-adaptive update. Extensive experiments across diverse PDE benchmarks and network architectures reveal a key insight: while powerful baselines like CMA-ES excel on smaller networks, their performance degrades significantly as the network capacity increases. In contrast, AMNES within MEES-PINN demonstrates superior scalability, consistently achieving better physically accurate solutions, as confirmed by quantitative metrics and qualitative visualization.