Related papers: Probabilistic machine learning based predictive an…

Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…

Digital Twins have emerged as a disruptive technology with great potential; they can enhance WDS by offering real-time monitoring, predictive maintenance, and optimization capabilities. This paper describes the development of a…

Soft robots, made from compliant materials, exhibit complex dynamics due to their flexibility and high degrees of freedom. Controlling soft robots presents significant challenges, particularly underactuation, where the number of inputs is…

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity PDE models governed by autonomous dynamical systems, leading to large-scale forward…

In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…

Change point detection becomes more and more important as datasets increase in size, where unsupervised detection algorithms can help users process data. To detect change points, a number of unsupervised algorithms have been developed which…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

Modern statistical learning techniques have often emphasized prediction performance over interpretability, giving rise to "black box" models that may be difficult to understand, and to generalize to other settings. We conceptually divide a…

In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…

Digital Twins (DTs) are becoming increasingly vital for future industrial applications, enhancing monitoring, control, and optimization of physical assets. This enhancement is made possible by integrating various Digital Models (DMs) within…

While the digital twin has become an intrinsic part of the product creation process, its true power lies in the connectivity of the digital representation with its physical counterpart. Data acquired on the physical asset can validate,…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

The report describes the discussions from the Workshop on Mathematical Opportunities in Digital Twins (MATH-DT) from December 11-13, 2023, George Mason University. It illustrates that foundational Mathematical advances are required for…

Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection…

This paper proposes a novel methodology for probabilistic dynamic security assessment and enhancement of power systems that considers load and generation variability, N-2 contingencies, and uncertain cascade propagation caused by uncertain…

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…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Human digital twins (HDTs) are dynamic, data-driven virtual representations of individuals, continuously updated with multimodal data to simulate, monitor, and predict health trajectories. By integrating clinical, physiological, behavioral,…

The demand for condition-based and predictive maintenance is rising across industries, especially for remote, high-value, and high-risk assets. In this article, the diagnostic digital twin concept is introduced, discussed, and implemented…