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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 …
Parameterized neural ordinary differential equations: Applications to computational physics problems
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 …
introducing an additional set of ODE input parameters to NODEs. This extension allows …
Reduced order models for Lagrangian hydrodynamics
As a mathematical model of high-speed flow and shock wave propagation in a complex
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …
multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes …
Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition
Abstract The Rayleigh-Taylor instability is a classical hydrodynamic instability of great
interest in various disciplines of science and engineering, including astrophysics …
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
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 …
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
This work presents a method for constructing online-efficient reduced models of large-scale
systems governed by parametrized nonlinear scalar conservation laws. The solution …
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
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 …
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
This work presents a method for constructing online-efficient reduced models of large-scale
systems governed by parametrized nonlinear scalar conservation laws. The solution …
systems governed by parametrized nonlinear scalar conservation laws. The solution …
Depth separation beyond radial functions
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 …
can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer …
A Low Rank Neural Representation of Entropy Solutions
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 …
laws with a smooth convex flux function in a single spatial dimension. The representation is …