相关论文: Error bound analysis of the stochastic parareal al…

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…

The main objective of this work is to investigate non-linear errors and pairwise summation using stochastic rounding (SR) in variance computation algorithms. We estimate the forward error of computations under SR through two methods: the…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…

Recently, stochastic rounding (SR) has been implemented in specialized hardware but most current computing nodes do not yet support this rounding mode. Several works empirically illustrate the benefit of stochastic rounding in various…

This paper discusses the non-parametric estimation of a non-linear reaction term in a semi-linear parabolic stochastic partial differential equation (SPDE). The estimator's consistency is due to the spatial ergodicity of the SPDE while the…

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often…

We prove the existence and uniqueness of solution of the obstacle problem for quasilinear stochastic partial differential equations (OSPDEs for short) with Neumann boundary condition. Our method is based on the analytical technics coming…

A parareal algorithm based on an exponential $\theta$-scheme is proposed for the stochastic Schr\"odinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential…

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…

We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…

This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…