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 …

Promoting global stability in data-driven models of quadratic nonlinear dynamics

AA Kaptanoglu, JL Callaham, A Aravkin, CJ Hansen… - Physical Review …, 2021 - APS
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 …

DPM: A novel training method for physics-informed neural networks in extrapolation

J Kim, K Lee, D Lee, SY Jhin, N Park - Proceedings of the AAAI …, 2021 - ojs.aaai.org
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 …

Universal physics transformers: A framework for efficiently scaling neural operators

B Alkin, A Fürst, S Schmid, L Gruber… - Advances in …, 2025 - proceedings.neurips.cc
Neural operators, serving as physics surrogate models, have recently gained increased
interest. With ever increasing problem complexity, the natural question arises: what is an …

Parameterized physics-informed neural networks for parameterized PDEs

W Cho, M Jo, H Lim, K Lee, D Lee, S Hong… - arxiv preprint arxiv …, 2024 - arxiv.org
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 …

Crom: Continuous reduced-order modeling of pdes using implicit neural representations

PY Chen, J **ang, DH Cho, Y Chang… - arxiv preprint arxiv …, 2022 - arxiv.org
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 …

Reduced-order modeling

Z Bai, PM Dewilde, RW Freund - Handbook of numerical analysis, 2005 - Elsevier
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 …

Non-linear manifold reduced-order models with convolutional autoencoders and reduced over-collocation method

F Romor, G Stabile, G Rozza - Journal of Scientific Computing, 2023 - Springer
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 …

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 …

Symplectic model reduction of Hamiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder

P Buchfink, S Glas, B Haasdonk - SIAM Journal on Scientific Computing, 2023 - SIAM
Classical model reduction techniques project the governing equations onto linear
subspaces of the high-dimensional state-space. For problems with slowly decaying …