Learning nonlinear reduced models from data with operator inference
B Kramer, B Peherstorfer… - Annual Review of Fluid …, 2024 - annualreviews.org
This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …
incorporates physical governing equations by defining a structured polynomial form for the …
Operator inference for non-intrusive model reduction with quadratic manifolds
This paper proposes a novel approach for learning a data-driven quadratic manifold from
high-dimensional data, then employing this quadratic manifold to derive efficient physics …
high-dimensional data, then employing this quadratic manifold to derive efficient physics …
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
Numerical simulations on fluid dynamics problems primarily rely on spatially or/and
temporally discretization of the governing equation using polynomials into a finite …
temporally discretization of the governing equation using polynomials into a finite …
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate
physical simulations in which the intrinsic solution space falls into a subspace with a small …
physical simulations in which the intrinsic solution space falls into a subspace with a small …
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …
Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
J Xu, K Duraisamy - Computer Methods in Applied Mechanics and …, 2020 - Elsevier
A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …
Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs
We make connections between complexity of training of physics-informed neural networks
(PINNs) and Kolmogorov n-width of the solution. Leveraging this connection, we then …
(PINNs) and Kolmogorov n-width of the solution. Leveraging this connection, we then …
Randomized sparse neural galerkin schemes for solving evolution equations with deep networks
J Berman, B Peherstorfer - Advances in Neural Information …, 2024 - proceedings.neurips.cc
Training neural networks sequentially in time to approximate solution fields of time-
dependent partial differential equations can be beneficial for preserving causality and other …
dependent partial differential equations can be beneficial for preserving causality and other …
Predictive reduced order modeling of chaotic multi-scale problems using adaptively sampled projections
C Huang, K Duraisamy - Journal of Computational Physics, 2023 - Elsevier
An adaptive projection-based reduced-order model (ROM) formulation is presented for
model-order reduction of problems featuring chaotic and convection-dominant physics. An …
model-order reduction of problems featuring chaotic and convection-dominant physics. An …
Crom: Continuous reduced-order modeling of pdes using implicit neural representations
The long runtime of high-fidelity partial differential equation (PDE) solvers makes them
unsuitable for time-critical applications. We propose to accelerate PDE solvers using …
unsuitable for time-critical applications. We propose to accelerate PDE solvers using …