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We compare two theoretically distinct approaches to generating artificial (or ``surrogate'') data for testing hypotheses about a given data set. The first and more straightforward approach is to fit a single ``best'' model to the original…
Robust Ordinal Regression (ROR) is a way of dealing with Multiple Criteria Decision Aiding (MCDA), by considering all sets of parameters of an assumed preference model, that are compatible with preference information given by the Decision…
This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct…
We analyze a lightweight simulation-based inference method that infers simulator parameters using only a regression-based projection of the observed data. After fitting a surrogate linear regression once, the procedure simulates small…
The a priori error analysis of reduced order models (ROMs) for fluids is relatively scarce. In this paper, we take a step in this direction and conduct numerical analysis of the recently introduced time relaxation ROM (TR-ROM), which uses…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
In this paper, we investigate the Gaussian graphical model inference problem in a novel setting that we call erose measurements, referring to irregularly measured or observed data. For graphs, this results in different node pairs having…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the ``Leitmotiv'' for the following. A reduced order model is…
Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a…
We present an introduction to some of the state of the art in reduced order and surrogate modeling in gravitational wave (GW) science. Approaches that we cover include Principal Component Analysis, Proper Orthogonal Decomposition, the…
A fundamental challenge in machine learning is the choice of a loss as it characterizes our learning task, is minimized in the training phase, and serves as an evaluation criterion for estimators. Proper losses are commonly chosen, ensuring…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for…
In this contribution, we focus on the Reynolds-Averaged Navier-Stokes (RANS) models and their exploitation to build reliable reduced order models to further accelerate predictions for real-time applications and many-query scenarios.…
Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a…
The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data relevant, e.g., for designing…