Related papers: Space-time reduced-order modeling for uncertainty …

We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…

Despite the strong predictive performance of deep learning models for traffic prediction, their widespread deployment in real-world intelligent transportation systems has been restrained by a lack of interpretability. Uncertainty…

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning…

Time encoding machines (TEMs) provide an event-driven alternative to classical uniform sampling, enabling power-efficient representations without a global clock. While prior work analyzed uniform quantization (UQ) of firing intervals, we…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question.…

An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

In aircraft design, structural optimization and uncertainty quantification concerning transonic aeroelastic issues are computationally impractical, because the iterative process requires great number of aeroelastic analysis. Emerging…

The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang--big crunch) at the quantum…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within…

This article proposes an PQR search method for probabilistic objects. The main idea of our method is to use a strategy called \textit{pre-approximation} that can reduce the initial problem to a highly simplified version, implying that it…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves…