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Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More…

The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and…

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in…

To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the…

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…

Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics…

Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…

This paper studies a Markov network model for unbalanced data, aiming to solve the problems of classification bias and insufficient minority class recognition ability of traditional machine learning models in environments with uneven class…

Dynamic community detection concerns inferring how community memberships evolve over time, including the emergence, persistence, merging, and dissolution of groups in temporal networks. We propose a Bayesian nonparametric model for…

Automated driving applications require accurate vehicle specific models to precisely predict and control the motion dynamics. However, modern vehicles have a wide array of digital and mechatronic components that are difficult to model,…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…