A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Y Kim, Y Choi, D Widemann, T Zohdi - Journal of Computational Physics, 2022 - Elsevier
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 …

Parameterized neural ordinary differential equations: Applications to computational physics problems

K Lee, EJ Parish - Proceedings of the Royal Society A, 2021 - royalsocietypublishing.org
This work proposes an extension of neural ordinary differential equations (NODEs) by
introducing an additional set of ODE input parameters to NODEs. This extension allows …

Reduced order models for Lagrangian hydrodynamics

DM Copeland, SW Cheung, K Huynh, Y Choi - Computer Methods in …, 2022 - Elsevier
As a mathematical model of high-speed flow and shock wave propagation in a complex
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …

Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

SW Cheung, Y Choi, DM Copeland, K Huynh - Journal of Computational …, 2023 - Elsevier
Abstract The Rayleigh-Taylor instability is a classical hydrodynamic instability of great
interest in various disciplines of science and engineering, including astrophysics …

Machine learning moment closure models for the radiative transfer equation I: Directly learning a gradient based closure

J Huang, Y Cheng, AJ Christlieb, LF Roberts - Journal of Computational …, 2022 - Elsevier
In this paper, we take a data-driven approach and apply machine learning to the moment
closure problem for the radiative transfer equation in slab geometry. Instead of learning the …

Manifold approximations via transported subspaces: Model reduction for transport-dominated problems

D Rim, B Peherstorfer, KT Mandli - arxiv preprint arxiv:1912.13024, 2019 - arxiv.org
This work presents a method for constructing online-efficient reduced models of large-scale
systems governed by parametrized nonlinear scalar conservation laws. The solution …

Machine learning moment closure models for the radiative transfer equation II: Enforcing global hyperbolicity in gradient-based closures

J Huang, Y Cheng, AJ Christlieb, LF Roberts… - Multiscale Modeling & …, 2023 - SIAM
This is the second paper in a series in which we develop machine learning (ML) moment
closure models for the radiative transfer equation (RTE). In our previous work [J. Huang, Y …

Manifold approximations via transported subspaces: Model reduction for transport-dominated problems

D Rim, B Peherstorfer, KT Mandli - SIAM Journal on Scientific Computing, 2023 - SIAM
This work presents a method for constructing online-efficient reduced models of large-scale
systems governed by parametrized nonlinear scalar conservation laws. The solution …

Depth separation beyond radial functions

L Venturi, S Jelassi, T Ozuch, J Bruna - Journal of machine learning …, 2022 - jmlr.org
High-dimensional depth separation results for neural networks show that certain functions
can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer …

A Low Rank Neural Representation of Entropy Solutions

D Rim, G Welper - arxiv preprint arxiv:2406.05694, 2024 - arxiv.org
We construct a new representation of entropy solutions to nonlinear scalar conservation
laws with a smooth convex flux function in a single spatial dimension. The representation is …