The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific phenomena, is one of the key techniques at the forefront of recent advances. PINNs are typically trained using stochastic gradient descent methods, akin to their deep learning counterparts. However, analysis in this paper shows that PINNs' unique loss formulations lead to a high degree of complexity and ruggedness that may not be conducive for gradient descent. Unlike in standard deep learning, PINN training requires globally optimum parameter values that satisfy physical laws as closely as possible. Spurious local optimum, indicative of erroneous physics, must be avoided. Hence, neuroevolution algorithms, with their superior global search capacity, may be a better choice for PINNs relative to gradient descent methods. Here, we propose a set of five benchmark problems, with open-source codes, spanning diverse physical phenomena for novel neuroevolution algorithm development. Using this, we compare two neuroevolution algorithms against the commonly used stochastic gradient descent, and our baseline results support the claim that neuroevolution can surpass gradient descent, ensuring better physics compliance in the predicted outputs. %Furthermore, implementing neuroevolution with JAX leads to orders of magnitude speedup relative to standard implementations.

翻译：学习模型在基础科学研究与发现领域的潜力正日益引起全球关注。物理信息神经网络（PINNs）是近期前沿进展的关键技术之一，其损失函数直接嵌入了科学现象的支配方程。与深度学习同类方法类似，PINNs通常使用随机梯度下降方法进行训练。然而，本文分析表明，PINNs独特的损失函数形式会导致高度的复杂性和粗糙性，这可能不利于梯度下降方法。与标准深度学习不同，PINNs训练需要全局最优参数值，以尽可能精确地满足物理定律。必须避免指示错误物理现象的虚假局部最优解。因此，具有优越全局搜索能力的神经进化算法，相对于梯度下降方法，可能更适合PINNs。本文提出了五个涵盖不同物理现象的基准问题，并提供了开源代码，用于新型神经进化算法的开发。基于此，我们将两种神经进化算法与常用的随机梯度下降方法进行比较，基线结果支持以下观点：神经进化可以超越梯度下降，确保预测输出具有更好的物理一致性。