Related papers: Data-driven non-Markovian closure models

In a real-life setting, little is known regarding the effectiveness of statins for primary prevention among older adults, and analysis of observational data can add crucial information on the benefits of actual patterns of use. Latent class…

State-space models (SSM) with Markov switching offer a powerful framework for detecting multiple regimes in time series, analyzing mutual dependence and dynamics within regimes, and asserting transitions between regimes. These models…

Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to learn the gradient of…

The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…

The generalized Langevin equation (GLE), derived by projection from a general many-body Hamiltonian, exactly describes the dynamics of an arbitrary coarse-grained variable in a complex environment. However, analysis and prediction of…

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum…

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features…

The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…

Multivariate probit models (MPM) have the appealing feature of capturing some of the dependence structure between the components of multidimensional binary responses. The key for the dependence modelling is the covariance matrix of an…

This paper addresses three complex control challenges related to input-saturated systems from a data-driven perspective. Unlike the traditional two-stage process involving system identification and model-based control, the proposed approach…

We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born-Markov or rotating wave approximations…

Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…

Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a…

Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical…

The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its…

This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied…

Performing analysis, optimization and control using simulations of many-particle systems is computationally demanding when no macroscopic model for the dynamics of the variables of interest is available. In case observations on the…

In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…

With the accumulation of data at an unprecedented rate, its potential to fuel scientific discovery is growing exponentially. This position paper urges the Machine Learning (ML) community to exploit the capabilities of large generative…