Related papers: Time-Dependent Low-Rank Input-Output Operator for …
Discovery of mathematical descriptors of physical phenomena from observational and simulated data, as opposed to from the first principles, is a rapidly evolving research area. Two factors, time-dependence of the inputs and hidden…
Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases…
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…
This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…
Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The approach, based on a dynamic mode…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
The trade-off between model fidelity and computational cost remains a central challenge in the computational modeling of extrusion-based 3D printing, particularly for real time optimization and control. Although high fidelity simulations…
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…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…