model reduction

Data-driven time parallelism via forecasting

This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time evolution …

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an …

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate …

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

This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the reduced-order-model …

Space–time least-squares Petrov–Galerkin projection for nonlinear model reduction

This work proposes a space--time least-squares Petrov--Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov--)Galerkin projection …

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 …

An efficient, globally convergent method for optimization under uncertainty using adaptive model reduction and sparse grids

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) …

Conservative model reduction for finite-volume models

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models …

Krylov-subspace recycling via the POD-augmented conjugate-gradient method

This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies …

Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, …