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This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art…

Numerical Analysis · Mathematics 2020-10-28 Peter Benner , Pawan Goyal , Boris Kramer , Benjamin Peherstorfer , Karen Willcox

We propose a parametric sampling strategy for the reduction of large-scale PDE systems with multidimensional input parametric spaces by leveraging models of different fidelity. The design of this methodology allows a user to adaptively…

Numerical Analysis · Mathematics 2023-01-24 Manisha Chetry , Domenico Borzacchiello , Lucas Lestandi , Luisa Rocha Da Silva

The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…

Optimization and Control · Mathematics 2026-04-28 Shreyas Bharadwaj , Bamdev Mishra , Cyrus Mostajeran , Alberto Padoan , Jeremy Coulson , Ravi N. Banavar

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Numerical Analysis · Mathematics 2023-11-30 Tianshu Wen , Kookjin Lee , Youngsoo Choi

In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…

Optimization and Control · Mathematics 2018-10-02 Alessandro Alla , Bernard Haasdonk , Andreas Schmidt

We present an optimal strategy having finite outcomes for estimating a single parameter of the displacement operator on an arbitrary finite dimensional system using a finite number of identical samples. Assuming the uniform {\it a priori}…

Quantum Physics · Physics 2009-11-06 M. Sasaki , A. Carlini , A. Chefles

This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Lantian Zhang , Bo Wahlberg , Silun Zhang

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

Methodology · Statistics 2023-08-02 Yong He , Ran Zhao , Wen-Xin Zhou

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…

Fluid Dynamics · Physics 2019-01-04 Nirmal J. Nair , Maciej Balajewicz

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Dynamical Systems · Mathematics 2017-07-07 Zoran Tomljanović , Christopher Beattie , Serkan Gugercin

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

Machine Learning · Statistics 2021-08-23 Patrick Héas , Cédric Herzet

In large-scale data processing scenarios, data often arrive in sequential streams generated by complex systems that exhibit drifting distributions and time-varying system parameters. This nonstationarity challenges theoretical analysis, as…

Machine Learning · Computer Science 2026-02-13 Yifei Jin , Xin Zheng , Lei Guo

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are…

Numerical Analysis · Mathematics 2013-04-09 Paul G. Constantine , Qiqi Wang

We introduce and study a variational framework for the analysis of empirical risk based inference for dynamical systems and ergodic processes. The analysis applies to a two-stage estimation procedure in which (i) the trajectory of an…

Dynamical Systems · Mathematics 2018-01-24 Kevin McGoff , Andrew B. Nobel

When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…

Numerical Analysis · Mathematics 2024-10-30 Ibrahima Dione

Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…

Methodology · Statistics 2018-04-10 German A. Schnaidt Grez , Brani Vidakovic

This paper presents adaptive bidirectional minimum mean-square error parameter estimation algorithms for fast-fading channels. The time correlation between successive channel gains is exploited to improve the estimation and tracking…

Information Theory · Computer Science 2015-10-14 P. Clarke , R. C. de Lamare

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Numerical Analysis · Mathematics 2021-10-22 Peter Sentz , Kristian Beckwith , Eric C. Cyr , Luke N. Olson , Ravi Patel

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

In this study the common least-squares minimization approach is compared to the Bayesian updating procedure. In the content of material parameter identification the posterior parameter density function is obtained from its prior and the…

Data Analysis, Statistics and Probability · Physics 2024-08-12 Thomas Most