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1. Robust data-driven discovery of governing physical laws with error bars

   https://doi.org/10.1098/rspa.2018.0305  

   Zhang, Sheng; Lin, Guang (September 2018, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier–Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the data-driven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions. 

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2. Continual Learning with Differential Privacy

   https://doi.org/10.1007/978-3-030-92310-5_39  

   Desai, Pradnya; Lai, Phung; Phan, NhatHai; Thai, My T. (October 2021, International Conference on Neural Information Processing)

   In this paper, we focus on preserving differential privacy (DP) in continual learning (CL), in which we train ML models to learn a sequence of new tasks while memorizing previous tasks. We first introduce a notion of continual adjacent databases to bound the sensitivity of any data record participating in the training process of CL. Based upon that, we develop a new DP-preserving algorithm for CL with a data sampling strategy to quantify the privacy risk of training data in the well-known Averaged Gradient Episodic Memory (A-GEM) approach by applying a moments accountant. Our algorithm provides formal guarantees of privacy for data records across tasks in CL. Preliminary theoretical analysis and evaluations show that our mechanism tightens the privacy loss while maintaining a promising model utility. 

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3. Meteor Detection With a New Computer Vision Approach

   https://doi.org/10.1029/2022RS007515  

   Li, Yanlin; Galindo, Freddy; Urbina, Julio; Zhou, Qihou; Huang, Tai‐Yin (October 2022, Radio Science)

   Abstract A novel computer vision‐based meteor head echo detection algorithm is developed to study meteor fluxes and their physical properties, including initial range, range coverage, and radial velocity. The proposed Algorithm for Head Echo Automatic Detection (AHEAD) comprises a feature extraction function and a Convolutional Neural Network (CNN). The former is tailored to identify meteor head echoes, and then a CNN is employed to remove false alarms. In the testing of meteor data collected with the Jicamarca 50 MHz incoherent scatter radar, the new algorithm detects over 180 meteors per minute at dawn, which is 2 to 10 times more sensitive than prior manual or algorithmic approaches, with a false alarm rate less than 1 percent. The present work lays the foundation of developing a fully automatic AI‐meteor package that detects, analyzes, and distinguishes among many types of meteor echoes. Furthermore, although initially evaluated for meteor data collected with the Jicamarca VHF incoherent radar, the new algorithm is generic enough that can be applied to other facilities with minor modifications. The CNN removes up to 98 percent of false alarms according to the testing set. We also present and discuss the physical characteristics of meteors detected with AHEAD, including flux rate, initial range, line of sight velocity, Signal‐to‐Noise Ratio, and noise characteristics. Our results indicate that stronger meteor echoes are detected at a slightly lower altitude and lower radial velocity than other meteors. 

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4. Stochastic AUC Optimization Algorithms With Linear Convergence

   Natole, Michael; Ying, Yiming; Lyu, Siwei (June 2019, Frontiers in applied mathematics and statistics)

   Area under the ROC curve (AUC) is a standard metric that is used to measure classification performance for imbalanced class data. Developing stochastic learning algorithms that maximize AUC over accuracy is of practical interest. However, AUC maximization presents a challenge since the learning objective function is defined over a pair of instances of opposite classes. Existing methods circumvent this issue but with high space and time complexity. From our previous work of redefining AUC optimization as a convex-concave saddle point problem, we propose a new stochastic batch learning algorithm for AUC maximization. The key difference from our previous work is that we assume that the underlying distribution of the data is uniform, and we develop a batch learning algorithm that is a stochastic primal-dual algorithm (SPDAM) that achieves a linear convergence rate. We establish the theoretical convergence of SPDAM with high probability and demonstrate its effectiveness on standard benchmark datasets. 

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5. Quantum Annealing via Path-Integral Monte Carlo With Data Augmentation

   https://doi.org/https://doi.org/10.1080/10618600.2020.1814787  

   Hu, Jianchang; Wang, Yazhen (April 2021, Journal of computational and graphical statistics)

   McCormick, Tyler (Ed.)

   This article considers quantum annealing in the Ising framework for solving combinatorial optimization problems. The path-integral Monte Carlo simulation approach is often used to approximate quantum annealing and implement the approximation by classical computers, which refers to simulated quantum annealing (SQA). In this article, we introduce a data augmentation scheme into SQA and develop a new algorithm for its implementation. The proposed algorithm reveals new insights on the sampling behaviors in SQA. Theoretical analyses are established to justify the algorithm, and numerical studies are conducted to check its performance and to confirm the theoretical findings. Supplementary materials for this article are available online. 

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