Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, such as fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse; a scenario that is true in many scientific fields. Nonetheless, neural networks offer a strong foundation to digest physical-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce underlying physics: (i) physics-guided neural networks (PgNN), (ii) physics-informed neural networks (PiNN) and (iii) physics-encoded neural networks (PeNN). These approaches offer unique advantages to accelerate the modeling of complex multiscale multi-physics phenomena. They also come with unique drawbacks and suffer from unresolved limitations (e.g., stability, convergence, and generalization) that call for further research. This study aims to present an in-depth review of the three neural network frameworks (i.e., PgNN, PiNN, and PeNN) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed; limitations are discussed; and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides a solid starting point for researchers and engineers to comprehend how to integrate different layers of physics into neural networks.