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 \url{https://github.com/chiuph/Baldwinian-PINN}.

翻译：物理信息神经网络（PINNs）处于科学机器学习的前沿，能够创建具备物理定律认知能力并可精确模拟这些定律的机器智能。然而，当前的PINNs通常针对单一物理任务进行训练，即使对于相似物理领域的新任务，也需要计算成本高昂的重新训练。为突破这一局限，本文提出了一种通过鲍德温演化框架提升PINNs泛化能力的开创性方法。受早熟物种神经发育的启发——这些物种已进化出快速学习、预测和响应环境的能力，我们设想PINNs能够通过预设连接强度，形成对高效学习物理规律的强偏置。本文提出了一种新颖的两阶段随机规划框架，将基于物理任务分布熟练度的进化选择压力与针对采样任务子集的终身学习相结合，从而实例化鲍德温效应。演化得到的鲍德温式PINNs在一系列经验性挑战问题实例中展现出快速且符合物理规律的预测能力：与基于梯度的最先进元学习方法相比，其预测精度提升超过一个数量级，而计算成本仅为其一小部分。例如，在求解扩散-反应方程时，精度提升了70倍，同时计算时间减少了700倍。因此，本文标志着PINNs作为可泛化物理求解器的元学习领域实现了重要跨越。示例代码发布于 \url{https://github.com/chiuph/Baldwinian-PINN}。