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Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing and opinion setting. We address the problem of learning of a spreading model such that the predictions generated…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven…
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…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is…
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but…
Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex…
Stochastic vegetation-water dynamical systems play a pivotal role in ecological stability, biodiversity, water resource management, and adaptation to climate change. This research proposes a machine learning-based method for analyzing rare…
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…