Reduced basis methods for time-dependent problems
Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …
study of real-world phenomena in applied science and engineering. Computational methods …
Neural Galerkin schemes with active learning for high-dimensional evolution equations
Deep neural networks have been shown to provide accurate function approximations in high
dimensions. However, fitting network parameters requires informative training data that are …
dimensions. However, fitting network parameters requires informative training data that are …
A robust second-order low-rank BUG integrator based on the midpoint rule
Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly
model order reduction for prohibitively large matrix differential equations. A core ingredient …
model order reduction for prohibitively large matrix differential equations. A core ingredient …
Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds
This work presents two novel approaches for the symplectic model reduction of high-
dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical …
dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical …
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 …
Constructing custom thermodynamics using deep learning
One of the most exciting applications of artificial intelligence is automated scientific
discovery based on previously amassed data, coupled with restrictions provided by known …
discovery based on previously amassed data, coupled with restrictions provided by known …
A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy
Deterministic models for radiation transport describe the density of radiation particles
moving through a background material. In radiation therapy applications, the phase space of …
moving through a background material. In radiation therapy applications, the phase space of …
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
This work focuses on the conservation of quantities such as Hamiltonians, mass, and
momentum when solution fields of partial differential equations are approximated with …
momentum when solution fields of partial differential equations are approximated with …
Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks
Mesh-based simulations play a key role when modeling complex physical systems that, in
many disciplines across science and engineering, require the solution to parametrized time …
many disciplines across science and engineering, require the solution to parametrized time …
Model reduction techniques for parametrized nonlinear partial differential equations
NC Nguyen - Error Control, Adaptive Discretizations, and …, 2024 - books.google.com
2. Hyper-reduction methods 2.1 Parametrized integrals 2.2 Empirical quadrature methods
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …