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1. Characterizing the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova with laser interferometric data: A neural network approach

   Casallas-Lagos, A; Antelis, J; Moreno, C; Zanolin, M; Mezzacappa, A; Szczepanczyk, M (October 2023, Physical review D)

   We present a methodology based on the implementation of a fully connected neural network algorithm to estimate the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova (CCSN). For this study, we selected a fully connected deep neural network (DNN) regression model because it can learn both linear and nonlinear relationships between the input and output data, it is more appropriate for handling large-dimensional input data, and it offers high performance at a low computational cost. To train the Machine Learning (ML) algorithm, we construct a training dataset using synthetic waveforms, and several CCSN waveforms are used to test the algorithm. We performed a first-order estimation of the high-frequency gravitational wave emission on real interferometric LIGO data from the second half of the third observing run (O3b) with a two detector network (L1 and H1). The relative error associated with the estimate of the slope of the resonant frequency versus time for the GW from CCSN signals is within 13% for the tested candidates included in this study up to different Galactic distances (1.0, 2.3, 3.1, 4.3, 5.4, 7.3, and 10 kpc). This method is, to date, the best estimate of the temporal evolution of the high-frequency emission in real interferometric data. Our methodology of estimation can be used in future studies focused on physical properties of the progenitor. The distances where comparable performances could be achieved for Einstein Telescope and Cosmic Explorer roughly rescale with the noise floor improvements. 

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2. Characterizing the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova with laser interferometric data: A neural network approach

   Casallas-Lagos, A; Antelis, J; Moreno, C; Zanolin, M; Mezzacappa, A; Szczepańczyk, M (October 2023, Physical review D)

   We present a methodology based on the implementation of a fully connected neural network algorithm to estimate the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova (CCSN). For this study, we selected a fully connected deep neural network (DNN) regression model because it can learn both linear and nonlinear relationships between the input and output data, it is more appropriate for handling large-dimensional input data, and it offers high performance at a low computational cost. To train the Machine Learning (ML) algorithm, we construct a training dataset using synthetic waveforms, and several CCSN waveforms are used to test the algorithm. We performed a first-order estimation of the high-frequency gravitational wave emission on real interferometric LIGO data from the second half of the third observing run (O3b) with a two detector network (L1 and H1). The relative error associated with the estimate of the slope of the resonant frequency versus time for the GW from CCSN signals is within 13% for the tested candidates included in this study up to different Galactic distances (1.0, 2.3, 3.1, 4.3, 5.4, 7.3, and 10 kpc). This method is, to date, the best estimate of the temporal evolution of the high-frequency emission in real interferometric data. Our methodology of estimation can be used in future studies focused on physical properties of the progenitor. The distances where comparable performances could be achieved for Einstein Telescope and Cosmic Explorer roughly rescale with the noise floor improvements. 

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3. Online Weak-form Sparse Identification of Partial Differential Equations

   Daniel A.Messenger, Emiliano Dall’Anese (January 2023, 3rd Annual Conference on Mathematical and Scientific Machine Learning)

   Bin Dong, Qianxiao Li (Ed.)

   This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs the identification task by processing solution snapshots that arrive sequentially. The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem. In particular, we do not regularize the ℓ0-pseudo-norm, instead finding that directly applying its proximal operator (which corresponds to a hard thresholding) leads to efficient online system identification from noisy data. We demonstrate the success of the method on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with time-varying wavespeed, and the linear wave equation, in one, two, and three spatial dimensions, respectively. In particular, our examples show that the method is capable of identifying and tracking systems with coefficients that vary abruptly in time, and offers a streaming alternative to problems in higher dimensions. 

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4. Online Weak-form Sparse Identification of Partial Differential Equations

   Messenger, Daniel; Dall’Anese, Emiliano; Bortz, David (July 2022, Proceedings of Mathematical and Scientific Machine Learning, PMLR)

   This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs the identification task by processing solution snapshots that arrive sequentially. The core of the method combines a weak-form discretization of candidate PDEs with an online proximal gradient descent approach to the sparse regression problem. In particular, we do not regularize the ℓ0 -pseudo-norm, instead finding that directly applying its proximal operator (which corresponds to a hard thresholding) leads to efficient online system identification from noisy data. We demonstrate the success of the method on the Kuramoto-Sivashinsky equation, the nonlinear wave equation with time-varying wavespeed, and the linear wave equation, in one, two, and three spatial dimensions, respectively. In particular, our examples show that the method is capable of identifying and tracking systems with coefficients that vary abruptly in time, and offers a streaming alternative to problems in higher dimensions. 

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5. Linearized binary regression

   https://doi.org/10.1109/CISS.2018.8362200  

   Lan, Andrew S.; Chiang, Mung; Studer, Christoph (March 2018, 52nd Annual Conference on Information Sciences and Systems (CISS))

   Probit regression was first proposed by Bliss in 1934 to study mortality rates of insects. Since then, an extensive body of work has analyzed and used probit or related binary regression methods (such as logistic regression) in numerous applications and fields. This paper provides a fresh angle to such well-established binary regression methods. Concretely, we demonstrate that linearizing the probit model in combination with linear estimators performs on par with state-of-the-art nonlinear regression methods, such as posterior mean or maximum aposteriori estimation, for a broad range of real-world regression problems. We derive exact, closed-form, and nonasymptotic expressions for the mean-squared error of our linearized estimators, which clearly separates them from nonlinear regression methods that are typically difficult to analyze. We showcase the efficacy of our methods and results for a number of synthetic and real-world datasets, which demonstrates that linearized binary regression finds potential use in a variety of inference, estimation, signal processing, and machine learning applications that deal with binary-valued observations or measurements. 

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