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High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
Healthcare data often come from multiple sites in which the correlations between confounding variables can vary widely. If deep learning models exploit these unstable correlations, they might fail catastrophically in unseen sites. Although…
Future grid scenario analysis requires a major departure from conventional power system planning, where only a handful of most critical conditions is typically analyzed. To capture the inter-seasonal variations in renewable generation of a…
The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to…
The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics…
Discerning how a mutation affects the stability of a protein is central to the study of a wide range of diseases. Machine learning and statistical analysis techniques can inform how to allocate limited resources to the considerable time and…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…
Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are…
Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
Evolving data streams induce joint nonstationarity in continual semantic segmentation, where semantic classes, input distributions, and supervision availability change simultaneously over time. This setting reflects practical structured…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
Stability selection is a popular method for improving feature selection algorithms. One of its key attributes is that it provides theoretical upper bounds on the expected number of false positives, E(FP), enabling false positive control in…
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…
Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a…
We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
This paper presents a constraint-guided deep learning framework for developing physically consistent health indicators in bearing prognostics and health management. Conventional data-driven methods often lack physical plausibility, while…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…