Physics Informed Deep Learning for Inverse Problems in Solid Mechanics
Project Description
Our work seeks to allow identification of the mechanical properties of a material (Young's modulus and Poisson's ratio) based upon sparse observation of displacements (e.g., using sensors) given known boundary data. By means of physics-informed neural networks, we will reconstruct the full displacement field in a manner that ensures physical laws are satisfied and our observations are respected. This deep learning approach simultaneously solves the inverse problem to identify the (not generally homogeneous) mechanical properties.
Summary of results
Physics Informed Neural Networks (PINNs) provide a machine learning (ML) framework that combines learning from data with the soft imposition of physical constraints, in the form of approximately satisfying relevant partial differential equations (PDE) or approximately minimizing an appropriate energy functional. In this work, we have applied PINNs to solve the inverse problem of identifying unknown (and inhomogeneous) material properties based upon the observed response to applied loads. We demonstrated that PINNs are capable of reconstructing the full spatial distribution of a system’s response from only a portion of the measured response field, estimating unknown material properties, and training a model grounded in the underlying physics described by differential equations. Furthermore, PINNs are also shown to be capable of handling aleatoric uncertainty, which stems from the presence of noisy data.
Has your project benefitted from using Bede?
We would not have been able to undertake the range and complexity of computational studies required for this work without access to Bede.
Publications
Deep learning for inverse material characterization. Yousef Ghaffari Motlagh, Farshid Fathi, John C. Brigham,Peter K. Jimack. Computer Methods in Applied Mechanics and Engineering, 436, 1 March 2025, 117650. https://doi.org/10.1016/j.cma.2024.117650