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Machine Learning and Computational Mathematics
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1639–1670
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Preface
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : p. 1639
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Dying ReLU and Initialization: Theory and Numerical Examples
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1671–1706
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Finite Neuron Method and Convergence Analysis
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1707–1745
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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1746–1767
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Deep Network Approximation Characterized by Number of Neurons
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1768–1811
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Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1812–1837
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Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1838–1885
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A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1886–1906
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Random Batch Algorithms for Quantum Monte Carlo Simulations
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1907–1936
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High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1937–1969
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Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1970–2001
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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2002–2041
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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2042–2074
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Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2075–2108
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Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2109–2138
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Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2139–2157
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Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2158–2179
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An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems
Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2180–2205