相关论文: Weak Collocation Regression method: fast reveal hi…

Progress toward a first-principles theory of plasticity and work-hardening is currently impeded by an insufficient picture of dislocation kinetics (the dynamic effect of driving forces in a given dislocation theory). This is because present…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable $y = w^T x + \epsilon$ and its corresponding vector of covariates $x \in R^k$ are only…

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

We discuss a coarse-grained approach to the computation of rare events in the context of grand canonical Monte Carlo (GCMC) simulations of self-assembly of surfactant molecules into micelles. The basic assumption is that the {\it…

Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…

A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density…

This paper deals with uncertainty propagation of general stochastic hybrid systems (GSHS) where the continuous state space is a compact Lie group. A computational framework is proposed to solve the Fokker-Planck (FP) equation that describes…

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…

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…

Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…

This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…

In text classification tasks, models often rely on spurious correlations for predictions, incorrectly associating irrelevant features with the target labels. This issue limits the robustness and generalization of models, especially when…

We propose to optimize neural networks with a uniformly-distributed random learning rate. The associated stochastic gradient descent algorithm can be approximated by continuous stochastic equations and analyzed within the Fokker-Planck…