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Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…

Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach employs structural causal models that postulate noisy functional relations among a set of interacting variables.…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…

We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for…

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily…

With the establishment of global biological monitor network and development of remote sensing technology, data won't be a limitation, but the variance brought by spatial heterogeneous and fractal will influence correlation coefficient…

A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…

In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing…

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables.…

Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…

Cross-sectional studies are widely prevalent since they are more feasible to conduct compared to longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying processes.…

Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and…