Related papers: Structure-preserving learning for multi-symplectic…
Recent work in scientific machine learning (SciML) has focused on incorporating partial differential equation (PDE) information into the learning process. Much of this work has focused on relatively "easy" PDE operators (e.g., elliptic and…
Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics to evolve in a low-dimensional subspace of the original…
This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
We present two novel classes of fully discrete energy-preserving algorithms for the sine-Gordon equation subject to Neumann boundary conditions. The cosine pseudo-spectral method is first used to develop structure-preserving spatial…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of…
Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems…
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After…
This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…
We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
Finite-dimensional truncations are routinely used to approximate partial differential equations (PDEs), either to obtain numerical solutions or to derive reduced-order models. The resulting discretized equations are known to violate certain…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…