相关论文: Weak Collocation Regression for Inferring Stochast…

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…

In this paper, we establish the weak averaging principle for stochastic functional partial differential equations (in short, SFPDEs) with H$\ddot{\text{o}}$lder continuous coefficients and infinite delay by a new generalized coupling…

We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving…

Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak…

In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real…

There exists a diversity of weak Local Linearization (LL) schemes for the integration of stochastic differential equations with additive noise, which differ with respect to the algorithm that is employed in the numerical implementation of…

We study the averaging principle for a family of multiscale stochastic dynamical systems. The fast and slow components of the systems are driven by two independent stable L\'evy noises, whose stable indexes may be different. The…

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…

Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…

This paper develops a model-based framework for continuous-time policy evaluation (CTPE) in reinforcement learning, incorporating both Brownian and L\'evy noise to model stochastic dynamics influenced by rare and extreme events. Our…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

This work focuses on the quantitative contraction rates for McKean-Vlasov stochastic differential equations (SDEs) with multiplicative noise. Under suitable conditions on the coefficients of the SDE, this paper derives explicit quantitative…

The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…

This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…

After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this PhD thesis focuses at establishing the Schauder estimates, a useful analytical tool to prove also the well-posedness…

Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is…