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Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…

This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to…

Time series domain adaptation aims to transfer the complex temporal dependence from the labeled source domain to the unlabeled target domain. Recent advances leverage the stable causal mechanism over observed variables to model the…

Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…

Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…

In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large…

When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The…

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…

Causal analyses of longitudinal data generally assume that the qualitative causal structure relating variables remains invariant over time. In structured systems that transition between qualitatively different states in discrete time steps,…

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…

We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…

Sociotechnological and geospatial processes exhibit time varying structure that make insight discovery challenging. This paper proposes a new statistical model for such systems, modeled as dynamic networks, to address this challenge. It…

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…

Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…