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We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…

Methodology · Statistics 2021-12-16 Fan Bu , Allison E. Aiello , Alexander Volfovsky , Jason Xu

We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as…

Dynamical Systems · Mathematics 2019-10-02 Dengfeng Wu , Miaomiao Fu , Jinqiao Duan

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

Machine Learning · Statistics 2018-02-14 Adrian Wills , Thomas Schön

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward as there are…

Probability · Mathematics 2012-03-01 David F. Anderson , Masanori Koyama

Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…

Dynamical Systems · Mathematics 2021-05-04 John D. Jakeman , Roland Pulch

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Machine Learning · Computer Science 2021-09-30 Lukas Köhs , Bastian Alt , Heinz Koeppl

Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these…

Probability · Mathematics 2016-10-03 François Giraud , Pierre Del Moral

This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training,…

Fluid Dynamics · Physics 2024-08-02 Minghan Chu

We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…

Neurons and Cognition · Quantitative Biology 2007-05-23 H. Soula , C. C. Chow

We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a…

Analysis of PDEs · Mathematics 2011-12-19 José Antonio Carrillo , Stéphane Cordier , Simona Mancini

In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…

Probability · Mathematics 2012-11-12 Thorbjörn Gudmundsson , Henrik Hult

Human activities generate various event sequences such as taxi trip records, bike-sharing pick-ups, crime occurrence, and infectious disease transmission. The point process is widely used in many applications to predict such events related…

Machine Learning · Computer Science 2024-01-30 Yoshiaki Takimoto , Yusuke Tanaka , Tomoharu Iwata , Maya Okawa , Hideaki Kim , Hiroyuki Toda , Takeshi Kurashima

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Dynamical Systems · Mathematics 2023-05-17 Nan Chen , Yinling Zhang

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods,…

Statistical Mechanics · Physics 2015-06-19 Jacob D. Stevenson , David J. Wales

In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…

Numerical Analysis · Mathematics 2025-10-14 Zi Wu , Yong-Liang Zhao , Xian-Ming Gu

Revision of the paper previously entitled "Learning a Machine for the Decision in a Partially Observable Markov Universe" In this paper, we are interested in optimal decisions in a partially observable universe. Our approach is to directly…

Optimization and Control · Mathematics 2007-06-13 Frederic Dambreville

Recent years have seen a substantial development of quantitative methods, mostly led by the computer science community with the goal of developing better machine learning applications, mainly focused on predictive modeling. However,…

Machine Learning · Computer Science 2021-03-02 Daniel Hain , Roman Jurowetzki

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the…

Other Condensed Matter · Physics 2009-11-11 Rosalind J. Allen , Daan Frenkel , Pieter Rein ten Wolde

Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…

Atmospheric and Oceanic Physics · Physics 2023-08-09 Matthew Bonas , Christopher K. Wikle , Stefano Castruccio

Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on…

Atmospheric and Oceanic Physics · Physics 2024-02-29 Benedikt Barthel Sorensen , Alexis Charalampopoulos , Shixuan Zhang , Bryce Harrop , Ruby Leung , Themistoklis Sapsis