Related papers: Data-Driven Enhanced Model Reduction for Bifurcati…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion,…
This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…
This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…
This paper reports an initial work on power system oscillation damping improvement using a data-driven online optimization method. An online oscillation damping optimization mod-el is proposed and formulated in a form solvable by the…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester~(J. Comput. Phys., 553 (2026), 114743),…
Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the…
Modelling of contact-rich tasks is challenging and cannot be entirely solved using classical control approaches due to the difficulty of constructing an analytic description of the contact dynamics. Additionally, in a manipulation task like…
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior…
Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…
We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…