Related papers: Infinite-dimensional bilinear and stochastic balan…
The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…
We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method,…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. We…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
The article is devoted to a new proof of the expansion for iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process. The above expansion is based on Hermite polynomials and generalized multiple…
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
Harmonic Balance is one of the most popular methods for computing periodic solutions of nonlinear dynamical systems. In this work, we address two of its major shortcomings: First, we investigate to what extent the computational burden of…
We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
We propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear interactions of localized waves in this setting. This problem…
We show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time…
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical…