model reduction

Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in [Freno, Carlberg, …

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) …

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 …

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 …