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 …
Universal physics transformers: A framework for efficiently scaling neural operators
Neural operators, serving as physics surrogate models, have recently gained increased
interest. With ever increasing problem complexity, the natural question arises: what is an …
interest. With ever increasing problem complexity, the natural question arises: what is an …
Parameterized physics-informed neural networks for parameterized PDEs
Complex physical systems are often described by partial differential equations (PDEs) that
depend on parameters such as the Reynolds number in fluid mechanics. In applications …
depend on parameters such as the Reynolds number in fluid mechanics. In applications …
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 …
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 …