Related papers: Structure-Preserving Model Reduction of Forced Ham…
We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i)…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
We discuss structure-preserving time discretization for nonlinear port-Hamiltonian systems with state-dependent mass matrix. Such systems occur, for instance, in the context of structure-preserving nonlinear model order reduction for…
In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…
Real physical systems are dissipative -- a pendulum slows, a circuit loses charge to heat -- and forecasting their dynamics from partial observations is a central challenge in scientific machine learning. We address the \emph{position-only}…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an…
We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify…
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom. This Slow-Fast Decomposition (SFD) enslaves exponentially…
In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…
The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…
Model reduction using the proper orthogonal decomposition (POD) method is applied to the dynamics of ferroelastic patches to study the first order square to rectangular phase transformations. Governing equations for the system dynamics are…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
We introduce a new definition of discrete-time port-Hamiltonian systems (PHS), which results from structure-preserving discretization of explicit PHS in time. We discretize the underlying continuous-time Dirac structure with the collocation…