Model reduction for the material point method via an implicit neural representation of the deformation map

Abstract

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. To represent the low-dimensional nonlinear manifold, we consider an implicit neural representation (INR) that parameterizes the material-point deformation map as a function of time. This enables the use of deep convolutional autoencoders for defining the nonlinear manifold, which has proven effective for model reduction in other settings. The proposed approach enables large-scale simulations to execute efficiently via model reduction, which is particularly important for virtual reality (VR) applications that require real-time performance. We demonstrate the method's ability to significantly outperform linear-subspace methods on benchmark solid-mechanics problems, including scenarios with large deformations and complex contact.