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Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…

Populations and Evolution · Quantitative Biology 2022-01-19 K. Bodova , E. Szep , N. H. Barton

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

Probability · Mathematics 2014-07-04 Jeffrey F. Collamore , Guoqing Diao , Anand N. Vidyashankar

In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…

Machine Learning · Statistics 2023-06-21 Yang Li , Shenglan Yuan , Linghongzhi Lu , Xianbin Liu

Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…

Neural and Evolutionary Computing · Computer Science 2024-12-05 Omar Rodríguez-Abreo , José Luis Aragón , Mario Alan Quiroz-Juárez

Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations, which can result in low training efficiency and unpredictable errors when applied to structures…

Computational Physics · Physics 2019-11-21 Jonathan Vandermause , Steven B. Torrisi , Simon Batzner , Yu Xie , Lixin Sun , Alexie M. Kolpak , Boris Kozinsky

We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling…

Quantum Physics · Physics 2018-02-21 C. Aghamohammadi , S. P. Loomis , J. R. Mahoney , J. P. Crutchfield

We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed…

Probability · Mathematics 2016-10-10 Lars Nørvang Andersen , Patrick J. Laub , Leonardo Rojas-Nandayapa

Berliner (Likelihood and Bayesian prediction for chaotic systems, J. Am. Stat. Assoc. 1991) identified a number of difficulties in using the likelihood function within the Bayesian paradigm which arise both for state estimation and for…

Data Analysis, Statistics and Probability · Physics 2016-12-30 Hailiang Du , Leonard A. Smith

Precise trajectory prediction in complex driving scenarios is essential for autonomous vehicles. In practice, different driving scenarios present varying levels of difficulty for trajectory prediction models. However, most existing research…

Artificial Intelligence · Computer Science 2024-10-22 Zhezhang Ding , Huijing Zhao

Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…

Machine Learning · Statistics 2019-10-09 Sreelekha Guggilam , S. M. Arshad Zaidi , Varun Chandola , Abani Patra

Tight estimates of exit/containment probabilities are of particular importance in many control problems. Yet, estimating the exit/containment probabilities is non-trivial: even for linear systems (Ornstein-Uhlenbeck processes), the…

Probability · Mathematics 2019-10-10 Quang-Cuong Pham , Bastien Mallein , Jean-Jacques Slotine

Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event…

Methodology · Statistics 2026-01-06 Dohyun Ahn , Huiyi Chen , Lewen Zheng

Extreme El Ni\~no events, such as occurred in 1997--1998, can induce severe weather on a global scale, with significant socioeconomic impacts that motivate efforts to understand them better. However, extreme El Ni\~no events are rare, and…

Atmospheric and Oceanic Physics · Physics 2025-12-30 Sarah Packman , Justin Finkel , Dorian S. Abbot , Eli Tziperman

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…

Computation · Statistics 2023-11-27 Timo Schorlepp , Shanyin Tong , Tobias Grafke , Georg Stadler

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…

Data Analysis, Statistics and Probability · Physics 2021-10-13 Igor A Khovanov

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

Chaotic Dynamics · Physics 2016-09-08 A. Yu. Shahverdian , A. V. Apkarian

This work studies the effectiveness of several machine learning techniques for predicting extreme events occurring in the flow around an airfoil at low Reynolds. For certain Reynolds numbers the aerodynamic forces exhibit intermittent…

Fluid Dynamics · Physics 2021-08-13 Samuel H. Rudy , Themistoklis P. Sapsis

In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…

Machine Learning · Computer Science 2024-10-08 Jan Achterhold , Joerg Stueckler

Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…

Methodology · Statistics 2025-07-16 Lorenzo Dell'Oro , Carlo Gaetan