Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

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In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

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We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

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In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems, symplectic model redu ...

During the past decade, model order reduction (MOR) has been successfully applied to reduce the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. S ...

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Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

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Structure-preserving approaches and data-driven closure modeling for model order reduction

Generalised Howe duality and injectivity of induction: the symplectic case

A b-symplectic slice theorem

TimeEvolver: A program for time evolution with improved error bound

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Structure-Preserving Reduced Basis Methods For Poisson Systems

Scattering Map for the Vlasov–Poisson System

Symplectic dynamical low rank approximation of wave equations with random parameters

Reduction of the sign problem near T=0 in quantum Monte Carlo simulations

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Dynamical Reduced Basis Methods for Hamiltonian Systems

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

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Dynamical Low Rank approximation of PDEs with random parameters

Structure preserving model reduction of parametric Hamiltonian systems

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems