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Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…

Quantitative Methods · Quantitative Biology 2024-09-24 Arshed Nabeel , Ashwin Karichannavar , Shuaib Palathingal , Jitesh Jhawar , David B. Brückner , Danny Raj M. , Vishwesha Guttal

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

Chaotic Dynamics · Physics 2025-11-07 Giulio Del Felice , Ludovico Theo Giorgini

Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data,…

Numerical Analysis · Mathematics 2024-01-23 Yuhuang Meng , Yue Qiu

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

Machine Learning · Statistics 2020-04-14 Xihaier Luo , Ahsan Kareem

We have developed a Bayesian optimization (BO) workflow that integrates intra-step noise optimization into automated experimental cycles. Traditional BO approaches in automated experiments focus on optimizing experimental trajectories but…

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of…

Numerical Analysis · Mathematics 2022-05-04 Urban Fasel , J. Nathan Kutz , Bingni W. Brunton , Steven L. Brunton

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

Machine Learning · Computer Science 2023-01-31 William Gilpin

We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of…

Machine Learning · Computer Science 2013-12-17 Daniel Golovin , Andreas Krause , Debajyoti Ray

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…

Machine Learning · Statistics 2026-02-18 Ayush Bharti , Charita Dellaporta , Yuga Hikida , François-Xavier Briol

This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions.…

Computation · Statistics 2024-09-04 Skyler Wu

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Numerical Analysis · Mathematics 2019-07-19 Suryanarayana Maddu , Bevan L. Cheeseman , Ivo F. Sbalzarini , Christian L. Müller

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should…

Quantitative Methods · Quantitative Biology 2020-01-13 Daniel Toker , Friedrich T. Sommer , Mark D'Esposito

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at…

Dynamical Systems · Mathematics 2024-02-28 Tapas Tripura , Satyam Panda , Budhaditya Hazra , Souvik Chakraborty

Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…

Machine Learning · Computer Science 2025-05-13 Nima Dehghani

Detecting distributional drift in high-dimensional data streams presents fundamental challenges: global comparison methods scale poorly, projection-based approaches lose geometric structure, and re-clustering methods suffer from identity…

Machine Learning · Computer Science 2026-02-18 Anantha Sharma

Bayesian optimisation is a sample-efficient search methodology that holds great promise for accelerating drug and materials discovery programs. A frequently-overlooked modelling consideration in Bayesian optimisation strategies however, is…

Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points.…

Methodology · Statistics 2026-02-11 Sigrunn H. Sørbye , Eirik Myrvoll-Nilsen , Håvard Rue

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Machine Learning · Statistics 2019-10-03 Geoffrey Roeder , Paul K. Grant , Andrew Phillips , Neil Dalchau , Edward Meeds

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by…

Machine Learning · Computer Science 2022-06-03 Hongpeng Zhou , Wei Pan

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

Dynamical Systems · Mathematics 2021-09-15 Ying-Cheng Lai