Abstract

Physics-Informed Neural Networks (PINNs) are a class of Deep Learning (DL) that incorporate a series of physical laws, frequently described in the form of partial differential equations (PDEs), to steer the learning towards the solution for sparse training datasets, which could not be plausible with classic DL algorithms. The prosperity of PINNs is attributed to substantial algorithmic advances (e.g., graph-based automated differentiation) and major software developments (e.g., TensorFlow , Keras). DL is best suited to recognize the mapping relations between inputs/outputs given a training dataset. A beneficial remedy can be offered by physics-informed deep learning, which provides the network model along with the laws of physics governing the system. This can rectify the issues associated with the missing ingredients induced by the sparsity of data, uncertainties, or other less understood factors. We explore the application of the Physics-Informed Neural Networks (PINNs) in a range of conventional geotechnical and structural engineering problems. An Airy-inspired PINNs solution is proposed for the analysis of foundation problems. As another improvement, Fourier series are elaborated to investigate the solution of plates deflection. We find that enriching the feature space using Airy stress functions/Fourier series can significantly improve the accuracy of PINN solutions for biharmonic PDEs. We construct custom physics-informed functions next which pertain to fundamental solutions of fracture mechanics. We show the proposed framework can easily captures the singular solution and characteristic parameters accurately on both noise-free and noisy data regimes. Finally, the application PINNs to forward and inverse analyses of pile-soil interaction problems is presented.

Biography

Mohammad is a lecturer in the School of Civil and Environmental Engineering at UNSW. He completed his PhD in Computational Geomechanics at Sharif University of Technology in 2015. He immediately joined UNSW as a research associate, where he is currently employed. He specializes in the thermo-hydro-mechanical coupling processes in saturated/unsaturated porous formations. His research interest is the development of robust numerical simulation frameworks for the analysis of fractured porous media using the state-of-the-art computational methods, such as Extended Finite Element Method (XFEM), Non-differentiable Energy Minimisation using Discontinuous Galerkin Method (DG), and Phase-field Method (PF). More recently, Mohammad investigates the application of deep learning in the study of complex mechanical response of geo-infrastructures by means of the Physics-Informed Neural Networks (PINNs). He is a Chief Investigator (CI) and Data Manager in the Research Hub on “Resilient and Intelligent Infrastructure Systems (RIIS)”, which aims to sustainability, serviceability, resilience, planning, decision making, and safe operations in geotechnical, structural, and mining engineering applications. He is also a CI in ARC Discovery Project (DP) entitled, Non-differentiable Energy Minimisation for Modelling Fractured Porous Media. Mohammad has been the recipient of the excellent paper award by International Association for Computer Methods and Advances in Geomechanics (IACMAG 2022) Junior Individuals, the best paper awards in the 3rd Australasian Conference on Computational Mechanics (ACCM 2019), best paper award in the 1st International Conference on Geomechanics and Geoenvironmental Engineering (iCGMGE 2017) Early Careers, and Bronze Medal in 13th scientific Olympiad of civil engineering (Iran, 2008).