2022/11/14 by Salah A Faroughi, Faroughi, Salah A, Nikhil Pawar +10 · 5 citations
Computer Science · Materials Science · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and ELM #Machine Learning in Materials Science #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2211.07377
openalex publication_date 2022/11/14 · openalex created_date 2022/11/23 · openalex updated_date 2026/07/28
Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including 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, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) 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 researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.