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Sensory processing is hard because the variables of interest are encoded in spike trains in a relatively complex way. A major goal in sensory processing is to understand how the brain extracts those variables. Here we revisit a common…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineering. The Sindy algorithm has proven effective in leveraging…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for…
The behavior of High-Impedance Faults (HIFs) in power distribution systems depends on multiple factors, making it a challenging disturbance to model. If enough data from real staged faults is provided, signal processing techniques can help…
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…
Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Robotic manipulation in dynamic and unstructured environments requires safety mechanisms that exploit what is known and what is uncertain about the world. Existing safety filters often assume full observability, limiting their applicability…
Networks pervade many disciplines of science for analyzing complex systems with interacting components. In particular, this concept is commonly used to model interactions between genes and identify closely associated genes forming…
We have developed a deep generative model that can produce accurate optical emission spectra and colour images of an ICP plasma using only the applied coil power, electrode power, pressure and gas flows as inputs -- essentially an empirical…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
A new approach to the sparse Canonical Correlation Analysis (sCCA)is proposed with the aim of discovering interpretable associations in very high-dimensional multi-view, i.e.observations of multiple sets of variables on the same subjects,…
In laser-driven indirect inertial confinement fusion (ICF), a hohlraum--a cavity constructed from high-Z materials--serves the purpose of converting laser energy into thermal x-ray energy. This process involves the interaction of…
Heterogeneity is a hallmark of many complex diseases. There are multiple ways of defining heterogeneity, among which the heterogeneity in genetic regulations, for example GEs (gene expressions) by CNVs (copy number variations) and…
A key challenge in the continual learning setting is to efficiently learn a sequence of tasks without forgetting how to perform previously learned tasks. Many existing approaches to this problem work by either retraining the model on…
Image decomposition plays a crucial role in various computer vision tasks, enabling the analysis and manipulation of visual content at a fundamental level. Overlapping images, which occur when multiple objects or scenes partially occlude…