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The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…

This paper proposes a generalised framework for density estimation in large networks with measurable spatiotemporal variance in edge weights. We solve the stochastic shortest path problem for a large network by estimating the density of the…

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…

Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…

This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter…

In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…

Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We…

We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks…

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…

We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…