Related papers: Data-Driven Model Reduction by Moment Matching for…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
Estimation of the number of species or unobserved classes from a random sample of the underlying population is a ubiquitous problem in statistics. In classical settings, the size of the sample is usually small. New technologies such as…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…
We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
In this paper, we develop a unified approach to study partial identification of a finite-dimensional parameter defined by a general moment model with incomplete data. We establish a novel characterization of the identified set for the true…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
There is a growing interest in data-driven control of nonlinear systems over the last years. In contrast to related works, this paper takes a step back and aims to solve the output matching problem, a problem closely related to the…