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Full-Text Articles in Physical Sciences and Mathematics
System Identification Through Lipschitz Regularized Deep Neural Networks, Elisa Negrini, Giovanna Citti, Luca Capogna
System Identification Through Lipschitz Regularized Deep Neural Networks, Elisa Negrini, Giovanna Citti, Luca Capogna
Mathematics Sciences: Faculty Publications
In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs x˙(t)=f(t,x(t)) directly from observed uniformly time-sampled data using a neural network. In contrast with other neural network-based approaches to this problem, we add a Lipschitz regularization term to our loss function. In the synthetic examples we observed empirically that this regularization results in a smoother approximating function and better generalization properties when compared with non-regularized models, both on trajectory and non-trajectory data, especially in presence of noise. In contrast with sparse regression approaches, since neural networks …
A Data Science Course For Undergraduates: Thinking With Data, Benjamin Baumer
A Data Science Course For Undergraduates: Thinking With Data, Benjamin Baumer
Mathematics Sciences: Faculty Publications
Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated array of data available in many settings. These data tend to be nontraditional, in the sense that they are often live, large, complex, and/or messy. A first course in statistics at the undergraduate level typically introduces students to a variety of techniques to analyze small, neat, and clean datasets. However, whether they pursue more formal training in statistics or not, many of these students will end up …