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PHYSICS INFORMED GRAPH NEURAL NETWORKS FOR INVERSE MODELING IN SOLID MECHANICS
In this project the student will attempt to embed relevant physics priors in graph neural networks (GNNs) with the goal of developing an inverse modeling framework for the prediction of the underlying material model of a system, given the labeled input (load/excitation) and the output (mechanical response) data.
Keywords: Keywords: Graph neural networks, Physics prior, finite element method
Motivation:
For real-time monitoring of mechanical systems, various sensors are employed. These sensors measure the mechanical response of a system for a known excitation or load. These signals are analyzed using various data-driven methods for anomaly detection. However, these methods cannot localize the detected fault in the system. Graph neural networks are a promising approach for fault detection and localization since the structure of the system is encoded as a graph (collection of interconnected nodes with edges) and learned functions parameterizing the mechanical behavior act locally on the edges and nodes of the graph.
Motivation: For real-time monitoring of mechanical systems, various sensors are employed. These sensors measure the mechanical response of a system for a known excitation or load. These signals are analyzed using various data-driven methods for anomaly detection. However, these methods cannot localize the detected fault in the system. Graph neural networks are a promising approach for fault detection and localization since the structure of the system is encoded as a graph (collection of interconnected nodes with edges) and learned functions parameterizing the mechanical behavior act locally on the edges and nodes of the graph.
To this end, in this project, we explore the framework of GNNs to invert the stress and strain fields on a 2D mesh, obtained from finite element analysis (FEA) simulations to predict the underlying material model in the mesh. The student is expected to work on the Mechanical MNIST data (which contains the stress and strain fields for a heterogenous material obtained from FEA simulations (figure 1). To achieve this, the graph neural network has to be embedded with various physics and geometric priors, for e.g., the equivariance of the stress and strain fields to the frame of reference. Moreover, various constraints can be applied to the learned model as regularization to the loss term, for e.g., the constraints derived from the conservation laws.
In the possible extension of the proposed project, the student is expected to work on the Mechanical MNIST crack path dataset (figure 2). The goal of this work is to predict the crack locations in the mesh given the stress and strain field responses for different prescribed loadings in the cracked and uncracked meshes.
To this end, in this project, we explore the framework of GNNs to invert the stress and strain fields on a 2D mesh, obtained from finite element analysis (FEA) simulations to predict the underlying material model in the mesh. The student is expected to work on the Mechanical MNIST data (which contains the stress and strain fields for a heterogenous material obtained from FEA simulations (figure 1). To achieve this, the graph neural network has to be embedded with various physics and geometric priors, for e.g., the equivariance of the stress and strain fields to the frame of reference. Moreover, various constraints can be applied to the learned model as regularization to the loss term, for e.g., the constraints derived from the conservation laws.
In the possible extension of the proposed project, the student is expected to work on the Mechanical MNIST crack path dataset (figure 2). The goal of this work is to predict the crack locations in the mesh given the stress and strain field responses for different prescribed loadings in the cracked and uncracked meshes.