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Reinforcement learning in non-stationary environments is challenging due to abrupt and unpredictable changes in dynamics, often causing traditional algorithms to fail to converge. However, in many real-world cases, non-stationarity has some…

To maximize future rewards in this ever-changing world, animals must be able to discover the temporal structure of stimuli and then anticipate or act correctly at the right time. How the animals perceive, maintain, and use time intervals…

Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…

Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…

Traditional Smooth Transition Autoregressive (STAR) models offer an effective way to model these dynamics through smooth regime changes based on specific transition variables. In this paper, we propose a novel approach by drawing an analogy…

Non-Markovian dynamics are commonly found in real-world environments due to long-range dependencies, partial observability, and memory effects. The Bellman equation that is the central pillar of Reinforcement learning (RL) becomes only…

Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in…

Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…

A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…

We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…

Hidden Markov jump processes are an attractive approach for modeling clinical disease progression data because they are explainable and capable of handling both irregularly sampled and noisy data. Most applications in this context consider…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Dynamic and evolving operational and economic environments present significant challenges for decision-making. We explore a simulation optimization problem characterized by non-stationary input distributions with regime-switching dynamics…

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in…

We consider the problem of learning graphical models, also known as Markov random fields (MRFs) from temporally correlated samples. As in many traditional statistical settings, fundamental results in the area all assume independent samples…

In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle…

Hidden Markov Model (HMM) is often regarded as the dynamical model of choice in many fields and applications. It is also at the heart of most state-of-the-art speech recognition systems since the 70's. However, from Gaussian mixture models…

We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning…