model reduction

Nonlinear model reduction for high- and low-consequence applications

Keynote at Model Reduction and Surrogate Modeling (MORe2024)

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 …

Projection-tree reduced-order modeling for fast n-body computations

This work proposes the projection-tree reduced-order model for accelerating n-body computations. N-body problems arise in many applications including molecular dynamics, astrophysics, and electromagnetics, and their computational cost scales …

Preconditioned least-squares Petrov–Galerkin reduced order models

This work proposes a preconditioning strategy for the least-squares Petrov–Galerkin (LSPG) reduced-order model. Preconditioning is critical for ensuring that the LSPG method produces accurate reduced-order models, particularly when the full-order …

Statistical closure modeling for reduced-order models of stationary systems by the ROMES method

This work proposes the ROMES (Reduced-Order-Model Error Surrogates) method for statistical closure modeling of reduced-order models for stationary systems. The method constructs statistical models to characterize the error incurred by reduced-order …

Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction

This work proposes a domain-decomposition approach for the least-squares Petrov–Galerkin (LSPG) reduced-order model. The DD-LSPG method enables reduced-order models to be constructed independently on subdomains of the computational domain, which …

Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection

This work proposes a constrained-optimization projection framework for preserving general physical properties in model reduction of dynamical systems. The method formulates the reduced-order model as a constrained optimization problem in which the …