Global Solutions To Stochastic Reaction-Diffusion Equations With Super-Linear Drift And Multiplicative Noise

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.

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 ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time -dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the ...

This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs. Structure ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...

Decentralized learning is appealing as it enables the scalable usage of large amounts of distributed data and resources (without resorting to any central entity), while promoting privacy since every user minimizes the direct exposure of their data. Yet, wi ...

Remote photoplethysmography (rPPG) using camera-based imaging has shown excellent potential recently in vital signs monitoring due to its contactless nature. However, the optimum filter selection for pre-processing rPPG data in signal conditioning is still ...

Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood H ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

This paper proposes a novel method to improve georeferencing of airborne laser scanning by improved trajectory estimation using Vehicle Dynamic Model. In Vehicle Dynamic Model (VDM), the relationship between the dynamics of the platform and control inputs ...

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

A multi-agent system consists of a collection of decision-making or learning agents subjected to streaming observations from some real-world phenomenon. The goal of the system is to solve some global learning or optimization problem in a distributed or dec ...

This paper introduces Wireless IoT-based Noise Cancellation (WINC) which defines a framework for leveraging a wireless network of IoT microphones to enhance active noise cancellation in noise-canceling headphones. The IoT microphones forward ambient noise ...

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible ...

As the world’s population grows in cities, urban dwellers spend a large amount of time inside their home, making housing health ever more important. Critical for residents’ health, the interactions between indoor residential environments and outdoor enviro ...

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

Diffusion is one of the most important phenomena studied in science ranging from physics to biology and, in abstract form, even in social sciences. In the field of materials science, diffusion in crystalline solids is of particular interest as it plays a p ...

Global Solutions To Stochastic Reaction-Diffusion Equations With Super-Linear Drift And Multiplicative Noise

Chat with Graph Search

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

Exploiting the Signal-Leak Bias in Diffusion Models

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks

Lattice Models and Conformal Field Theory

Spectral Estimators for High-Dimensional Matrix Inference

A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects

The Privacy Power of Correlated Noise in Decentralized Learning

Optimal digital filter selection for remote photoplethysmography (rPPG) signal conditioning

Disentangling 1/f noise from confined ion dynamics

Functional data analysis with rough sample paths?

Model-based constraints for trajectory determination of quad-copters: Design, calibration & merits for direct orientation

Universal and adaptive methods for robust stochastic optimization

Multi-agent Learning with Privacy Guarantees

WINC: A Wireless IoT Network for Multi-Noise Source Cancellation

Koopman analysis of the periodic Korteweg-de Vries equation

Housing, street and health: a new systemic research framework

Tensor approximation of the self-diffusion matrix of tagged particle processes

Distributionally Robust Linear Quadratic Control

Atomic scale volume and grain boundary diffusion elucidated by in situ STEM