Related papers: Structure preserving discretization: A Berezin-Toe…
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…
We study extended Berezin and Berezin-Toeplitz quantization for compact Kaehler manifolds, two related quantization procedures which provide a general framework for approaching the construction of fuzzy compact Kaehler geometries. Using…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
We derive mixed finite element discretizations of a cold relativistics fluid model from approximations of the Poisson bracket that preserve mass, energy and the divergence constraints. For time-discretization we derive an implicit…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
In this paper we derive a Toeplitz-structured closed form of the unique positive semi-definite stabilizing solution for the discrete-time algebraic Riccati equations, especially for the case that the state matrix is not stable. Based on the…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
A majority of established quantum generalizations of discrete structures are shown to be instances of a single quantum generalization. In particular, the quantum graphs of Duan, Severini and Winter, the quantum metric spaces of Kuperberg…
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 investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
We prove a general theorem on the stochastic convergence of appropriately renormalized models arising from nonlinear stochastic PDEs. The theory of regularity structures gives a fairly automated framework for studying these problems but…
Designing controllers to satisfy temporal requirements has proven to be challenging for dynamical systems that are affected by uncertainty. This is mainly due to the states evolving in a continuous uncountable space, the stochastic…
We consider a general discretization strategy for Hamiltonian field theories generated by Lie-Poisson brackets which we call dual PIC (DPIC). This method involves prescribing two different discrete representations of the dynamical variable…
In this work we present a structure preserving discretization for turbidity currents based on a mass-, energy-, enstrophy-, and vorticity-conserving formulation for 2D incompressible flows. This discretization exploits a dual-field…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case.…
Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…