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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…
The Earth's turbulent atmosphere results in speckled and blurred images of astronomical objects when observed by ground based visible and near-infrared telescopes. Adaptive optics (AO) systems are employed to reduce these atmospheric…
The dynamic time scan forecasting method relies on the premise that the most important pattern in a time series precedes the forecasting window, i.e., the last observed values. Thus, a scan procedure is applied to identify similar patterns,…
In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly…
The increasingly populated cities of the 21st Century face the challenge of being sustainable and resilient spaces for their inhabitants. However, climate change, among other problems, makes these objectives difficult to achieve. The Urban…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios…
Diabetes foot ulceration (DFU) and amputation are a cause of significant morbidity. The prevention of DFU may be achieved by the identification of patients at risk of DFU and the institution of preventative measures through education and…
The Earth's atmosphere is comprised of turbulent layers that result in speckled and blurry images from ground-based visible and infrared observations. Adaptive Optics (AO) systems are employed to measure the perturbed wavefront with a…
Causal discovery algorithms based on probabilistic graphical models have emerged in geoscience applications for the identification and visualization of dynamical processes. The key idea is to learn the structure of a graphical model from…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
Distribution system state estimation (DSSE) is an essential tool for operation of distribution networks, the results of which enables the operator to have a thorough observation of the system. Thus, most distribution management systems…
Perception systems provide a rich understanding of the environment for autonomous systems, shaping decisions in all downstream modules. Hence, accurate detection and isolation of faults in perception systems is important. Faults in…
This paper presents a mathematical framework for modeling the dynamic effects of three fault categories and six fault variants in the ink channels of high-end industrial printers. It also introduces a hybrid approach that combines…
Geostationary satellites collect high-resolution weather data comprising a series of images which can be used to estimate wind speed and direction at different altitudes. The Derived Motion Winds (DMW) Algorithm is commonly used to process…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
The fundamental diagram (FD), also known as the flow--density relation, is one of the most fundamental concepts in the traffic flow theory. It describes the relation between equilibrated flow, density, and speed in traffic flow.…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
Diffusion tensor imaging (DTI) holds significant importance in clinical diagnosis and neuroscience research. However, conventional model-based fitting methods often suffer from sensitivity to noise, leading to decreased accuracy in…