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Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor…

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…

Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories…

This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…

Model reduction techniques have emerged as a powerful paradigm across different fronts of scientific computing. Despite their success, the provided tools and methodologies remain limited if high-dimensional dynamical systems subject to…

Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less…

We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…

Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a…

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…

Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum…

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…

Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened, or aggregated. As the neglected and unresolved terms become important, the utility of model predictions…

Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for observables of stochastic dynamical systems, we show that the obtained semigroup estimates for the EMZ equation can be used to drive prior estimates of…

Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…