Evolutionary Neural Architecture Search for Physics-Informed Neural Networks with Variable-Length Designs
提出Evo-NAS-PINN框架，通过两阶段搜索和自注意力代理模型高效探索变长架构，在偏微分方程求解中超越传统PINN基线，且无需额外数据即可泛化到新场景。
Physics-informed neural networks (PINNs) are a promising approach for solving partial differential equations (PDEs), but practical tuning remains largely handcrafted and costly, especially in variable-length search spaces where candidate architectures differ in depth and width. We present Evo-NAS-PINN, an evolutionary neural architecture search framework that addresses both the high per-candidate evaluation cost and the challenges posed by variable-length designs. Evo-NAS-PINN follows a two-stage scheme in which the last layer is cast as a convex regression solved in closed form via a gradient-free, physics-informed pseudo-inverse, while only the representation layers undergo a small number of gradient steps, greatly reducing evaluation cost during search. To explore variable-length designs efficiently, we introduce a self-attention-based surrogate-assisted evolutionary algorithm that encodes each architecture as a token sequence, uses attention to summarize sequences of different lengths, and provides uncertainty-aware guidance to the evolutionary loop. Across diverse PDE families, Evo-NAS-PINN delivers consistently better performance with only tens to a few hundred of optimization steps, surpassing strong PINN baselines that require prolonged training. Beyond efficiency, it generalizes robustly to previously unseen settings without additional data or retraining, and extensive experiments demonstrate its effectiveness and scalability for physics-informed architecture discovery.