Related papers: Structure-preserving learning for multi-symplectic…
Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning…
Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…
In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
Energy preserving numerical methods for a certain class of PDEs are derived, applying the partition of unity method. The methods are extended to also be applicable in combination with moving mesh methods by the rezoning approach. These…
We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation. We demonstrate that the scheme conserves energy up to machine precision. In this sense the method is consistent with the…
Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…
Developing accurate dynamical system models from physical insight or data can be impeded when only partial observations of the system state are available. Here, we combine conservation laws used in physics and engineering with artificial…
In this paper, reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schr\"odinger equation (NLSE) with and without damping. Both ALEs are non-canonical…
This study presents a hybrid reduced-order modeling (ROM) framework for turbulent incompressible flows on collocated finite volume grids. The methodology employs the "discretize-then-project" consistent flux strategy, which ensures mass…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based…
In this paper, we develop a high order structure-preserving local discontinuous Galerkin (DG) scheme for the compressible self-gravitating Euler equations, which pose great challenges due to the presence of time-dependent gravitational…
Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…