deep learning

LiCROM: Linear-subspace continuous reduced order modeling with neural fields

We propose LiCROM, a method that combines linear-subspace model reduction with continuous neural field representations. By representing the reduced basis using neural fields, we enable continuous queries in space and time, facilitating …

Neural stress fields for reduced-order elastoplasticity and fracture

We propose neural stress fields, a method for reduced-order modeling of elastoplastic materials and fracture mechanics. By representing stress fields using neural networks, we enable efficient simulation of complex material behaviors including …

CROM: Continuous reduced-order modeling of PDEs using implicit neural representations

We propose CROM (Continuous Reduced-Order Modeling), a framework for model reduction of PDEs using implicit neural representations. By leveraging coordinate-based neural networks, CROM represents the solution manifold continuously in both space and …

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

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 …

Deep Conservation: A latent dynamics model for exact satisfaction of physical conservation laws

This work proposes an approach for latent dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, we compute a low-dimensional embedding of the high-dimensional dynamical-system state using deep …

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis …

Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning

Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any time …