Related papers: Reduced-Order Modeling Of Hidden Dynamics
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…
We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates,…
We present a new reduced-order computational method for the molecular dynamics simulation of entangled polymer systems. The polymer chains are modeled as continuous Gaussian chains. Our algorithm is based on the application of the molecular…
A Markov decision process-based state switching is devised, implemented, and analyzed for proximity operations of various autonomous vehicles. The framework contains a pose estimator along with a multi-state guidance algorithm. The unified…
Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This…
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…
The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Berm\'udez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes…
Although major advances have been achieved over the past decades for the reduction and identification of linear systems, deriving nonlinear low-order models still is a chal- lenging task. In this work, we develop a new data-driven framework…
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through…
In safety-critical Cyber-Physical Systems (CPS), accurate trajectory prediction provides vital guidance for downstream planning and control, yet although deep learning models achieve high-fidelity forecasts on validation data, their…
The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
In this paper, the feasibility of recently developed higher order delayed sliding mode controllers is addressed. With this aim the robustness against the measurement noise and mismatched perturbations for the systems governed by such…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
Proper-orthogonal decomposition (POD) based reduced-order models (ROM) of structurally dominant fluid flow can support a wide range of engineering applications. Yet, although they perform well for unsteady laminar flows, their…
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…