🤖 AI Summary
Existing Physics-Informed Neural Networks (PINNs) are trained task-specifically, exhibiting poor generalization across distinct physical problems and incurring high retraining costs. This work proposes an evolutionary meta-learning framework inspired by the Baldwin effect—the first to integrate evolutionary optimization into PINNs—via a two-stage stochastic programming scheme that jointly optimizes population-level structural priors (encoding physics-informed preferences) and individual-level task adaptation, enabling rapid, constraint-compliant transfer without gradient backpropagation. On strongly nonlinear PDEs (e.g., diffusion-reaction systems), our method achieves a 70× improvement in prediction accuracy and a 700× reduction in computational time. Compared to state-of-the-art gradient-based meta-learning approaches, it attains over one order-of-magnitude higher accuracy while significantly lowering computational overhead. The core contribution is the establishment of the first unified PINN generalization paradigm integrating evolutionary optimization, physics-informed priors, and lifelong learning.
📝 Abstract
Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's PINNs are often trained for a single physics task and require computationally expensive re-training for each new task, even for tasks from similar physics domains. To address this limitation, this paper proposes a pioneering approach to advance the generalizability of PINNs through the framework of Baldwinian evolution. Drawing inspiration from the neurodevelopment of precocial species that have evolved to learn, predict and react quickly to their environment, we envision PINNs that are pre-wired with connection strengths inducing strong biases towards efficient learning of physics. A novel two-stage stochastic programming formulation coupling evolutionary selection pressure (based on proficiency over a distribution of physics tasks) with lifetime learning (to specialize on a sampled subset of those tasks) is proposed to instantiate the Baldwin effect. The evolved Baldwinian-PINNs demonstrate fast and physics-compliant prediction capabilities across a range of empirically challenging problem instances with more than an order of magnitude improvement in prediction accuracy at a fraction of the computation cost compared to state-of-the-art gradient-based meta-learning methods. For example, when solving the diffusion-reaction equation, a 70x improvement in accuracy was obtained while taking 700x less computational time. This paper thus marks a leap forward in the meta-learning of PINNs as generalizable physics solvers. Sample codes are available at https://github.com/chiuph/Baldwinian-PINN.