Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast EAs as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.

翻译：在有限数据上训练的深度学习模型缺乏对物理世界的完整理解。另一方面，物理信息神经网络（PINNs）通过将数学可表达的自然定律纳入其训练损失函数，注入了此类知识。通过遵循物理定律，PINNs在数据有限的情况下相比纯数据驱动模型具有优势，并展现出通往物理人工智能的有前景路径。这一特性将其推向了科学机器学习的前沿——该领域以数据稀缺且获取成本高昂为特征。然而，实现精确物理信息学习的愿景伴随着重大挑战。本研究从模型优化与泛化角度审视PINNs，揭示了需要新的算法进展以克服当前PINN模型在训练速度、精度和泛化能力方面的问题。特别值得关注的是利用无梯度进化算法（EAs）来优化PINN训练中特有的复杂损失函数景观。将梯度下降与EAs协同用于发现定制化神经网络架构、平衡物理信息学习目标中多项损失项的方法，被定位为未来研究的重要方向。另一条令人兴奋的路径是将EAs作为可泛化PINN模型的元学习器。为验证这些研究方向，我们进一步引述近期文献成果，展示此类方法在应对前述PINN优化与泛化挑战中取得的早期成功。