Machine learning for fast and reliable solution of time-dependent differential equations

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Throughout history, the pace of knowledge and information sharing has evolved into an unthinkable speed and media. At the end of the XVII century, in Europe, the ideas that would shape the "Age of Enlightenment" were slowly being developed in coffeehouses, ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

This dataset contains a collection of ultrafast ultrasound acquisitions from nine volunteers and the CIRS 054G phantom. For a comprehensive understanding of the dataset, please refer to the paper: Viñals, R.; Thiran, J.-P. A KL Divergence-Based Loss for In ...

Cells are the smallest operational units of living systems. Through synthesis of various biomolecules and exchange of signals with the environment, cells tightly regulate their composition to realize a specific functional state. The transformation of a cel ...

This article describes a field-based analytical model of single-sided linear induction motors (SLIMs) that explicitly considers the following effects altogether: finite motor length, magnetomotive force mmf space harmonics, slot effect, edge effect, and ta ...

Traditional cell cultures have long been fundamental to biological research, offering an alternative to animal models burdened by ethical constraints and procedural intricacies, often lacking relevance to human physiology and disease. Moreover, their inabi ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

Transformer models such as GPT generate human-like language and are predictive of human brain responses to language. Here, using functional-MRI-measured brain responses to 1,000 diverse sentences, we first show that a GPT-based encoding model can predict t ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are obtained in this ...

Machine learning for fast and reliable solution of time-dependent differential equations

Chat with Graph Search

Machine Learning for Modeling Stock Returns

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Generalization of Scaled Deep ResNets in the Mean-Field Regime

From low-rank retractions to dynamical low-rank approximation and back

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Anomalous dissipation and other non-smooth phenomena in fluids

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (5/6)

Deciphering the nature of cell state transitions in single cells using quantitative modeling of temporal dynamics

Analytical Model of Single-Sided Linear Induction Motors for High-Speed Applications

Accessible and highly observable gastrointestinal organoid model systems for studying host-pathogen interactions

Random matrix methods for high-dimensional machine learning models

Driving and suppressing the human language network using large language models

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Reliable data-driven decision-making through optimal transport

Boosting likelihood learning with event reweighting