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This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological…

This manuscript presents an advanced framework for Bayesian learning by incorporating action and state-dependent signal variances into decision-making models. This framework is pivotal in understanding complex data-feedback loops and…

In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…

Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in…

We demonstrate a machine learning based approach which can learn the time-dependent electronic excitation dynamics of small molecules subjected to ion irradiation. Ensembles of recurrent neural networks are trained on data generated by…

Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…

This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…

Combining the increasing availability and abundance of healthcare data and the current advances in machine learning methods have created renewed opportunities to improve clinical decision support systems. However, in healthcare risk…

We propose a scalable, approximate inference hypernetwork framework for a general model of history-dependent processes. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of…

Predicting a driver's cognitive state, or more specifically, modeling a driver's reaction time (RT) in response to the appearance of a potential hazard warrants urgent research. In the last two decades, the electric field that is generated…

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…