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 …
Promoting global stability in data-driven models of quadratic nonlinear dynamics
Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of
reduced-order models for a variety of scientific and engineering tasks. However, it is …
reduced-order models for a variety of scientific and engineering tasks. However, it is …
DPM: A novel training method for physics-informed neural networks in extrapolation
We present a method for learning dynamics of complex physical processes described by
time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in …
time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in …
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 …
Reduced-order modeling
In recent years, reduced-order modeling techniques have proven to be powerful tools for
various problems in circuit simulation. For example, today, reduction techniques are …
various problems in circuit simulation. For example, today, reduction techniques are …
Non-linear manifold reduced-order models with convolutional autoencoders and reduced over-collocation method
Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of
the model of interest can result in a slow Kolmogorov n-width decay, which precludes the …
the model of interest can result in a slow Kolmogorov n-width decay, which precludes the …
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 …
Symplectic model reduction of Hamiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder
Classical model reduction techniques project the governing equations onto linear
subspaces of the high-dimensional state-space. For problems with slowly decaying …
subspaces of the high-dimensional state-space. For problems with slowly decaying …
Efficient nonlinear manifold reduced order model
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 …