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In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…
The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…
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…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as…
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…
Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…
Schr\"odinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…
Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…
Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…
Reinforcement learning in multiagent systems has been studied in the fields of economic game theory, artificial intelligence and statistical physics by developing an analytical understanding of the learning dynamics (often in relation to…