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We introduce a machine-learning-based coarse-grained molecular dynamics (CGMD) model that faithfully retains the many-body nature of the inter-molecular dissipative interactions. Unlike common empirical CG models, the present model is…
In this paper, a combination of Galerkin's method and Dafermos' transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next,…
For infinite-horizon average-cost criterion problems, there exist relatively few rigorous approximation and reinforcement learning results. In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide…
Imitation learning considerably simplifies policy synthesis compared to alternative approaches by exploiting access to expert demonstrations. For such imitation policies, errors away from the training samples are particularly critical. Even…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
We study finite memory belief approximation for partially observable (PO) stochastic optimal control (SOC) problems. While belief states are sufficient for SOC in partially observable Markov decision processes (POMDPs), they are generally…
The stochastic Landau--Lifshitz--Gilbert (LLG) equation coupled with the Maxwell equations (the so called stochastic MLLG system) describes the creation of domain walls and vortices (fundamental objects for the novel nanostructured magnetic…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational…
The reinforcement learning algorithm SARSA combined with linear function approximation has been shown to converge for infinite horizon discounted Markov decision problems (MDPs). In this paper, we investigate the convergence of the…
In this study, we employ the recently developed recurrence microstate probabilities as features to improve accuracy of several well-established machine learning (ML) algorithms. These algorithms are applied to classify discrete and…
Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good…
We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…
Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…
Partially observed control problems are a challenging aspect of reinforcement learning. We extend two related, model-free algorithms for continuous control -- deterministic policy gradient and stochastic value gradient -- to solve partially…
Online reinforcement learning agents are currently able to process an increasing amount of data by converting it into a higher order value functions. This expansion of the information collected from the environment increases the agent's…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…