Related papers: Continuous Data Assimilation Reduced Order Models …
We investigate both theoretically and numerically the consistency between the nonlinear discretization in full order models (FOMs) and reduced order models (ROMs) for incompressible flows. To this end, we consider two cases: (i) FOM-ROM…
Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We…
This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…
Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and…
In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…
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…
Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…
Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…
Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…
This research paper investigates the Adjoint Petrov-Galerkin (APG) method for reduced order models (ROM) and fluid dynamics governed by the incompressible Navier-Stokes equations. The Adjoint Petrov-Galerkin ROM, derived using the…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "data assimilation window" separate from the observational…
Much sequential data exhibits highly non-uniform information distribution. This cannot be correctly modeled by traditional Long Short-Term Memory (LSTM). To address that, recent works have extended LSTM by adding more activations between…
Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system…
In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature. In this algorithm, we incorporate the observables as a…
Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…