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The possibility of using the Eulerian discretization for the problem of modelling high-dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to…
In this paper, we apply a supervised machine-learning approach to solve a fundamental problem in queueing theory: estimating the transient distribution of the number in the system for a G(t)/GI/1. We develop a neural network mechanism that…
In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of…
Networks-on-chip (NoCs) have become the standard for interconnect solutions in industrial designs ranging from client CPUs to many-core chip-multiprocessors. Since NoCs play a vital role in system performance and power consumption,…
Demand response management has become one of the key enabling technologies for smart grids. Motivated by the increasing demand response incentives offered by service operators, more customers are subscribing to various demand response…
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution…
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…
We develop a Bayesian inference method for discretely-observed stochastic differential equations (SDEs). Inference is challenging for most SDEs, due to the analytical intractability of the likelihood function. Nevertheless, forward…
Machine learning techniques are powerful tools for construction of emulators for complex systems. We explore different machine learning methods and conceptual methodologies, ranging from functional approximations to dynamical…
Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the…
In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure…