Found 18 Documents (Results 1–18)
Learning to discretize: solving 1D scalar conservation laws via deep reinforcement learning. (English) Zbl 1473.65124
Multi-scale deep neural network (MscaleDNN) methods for oscillatory Stokes flows in complex domains. (English) Zbl 1473.35541
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. (English) Zbl 1473.65251
MSC:
65M75
Convolution neural network shock detector for numerical solution of conservation laws. (English) Zbl 1528.65092
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. (English) Zbl 1473.65349
Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. (English) Zbl 1542.65182
Multi-scale deep neural network (MscaleDNN) for solving Poisson-Boltzmann equation in complex domains. (English) Zbl 1473.65348
Commun. Comput. Phys. 28, No. 5, 1970-2001 (2020); correction ibid. 33, No. 5, 1509-1513 (2023).
High-dimensional nonlinear multi-fidelity model with gradient-free active subspace method. (English) Zbl 1477.62094
A multi-scale DNN algorithm for nonlinear elliptic equations with multiple scales. (English) Zbl 1474.65445
Butterfly-net: optimal function representation based on convolutional neural networks. (English) Zbl 1507.68271
Multifidelity data fusion via gradient-enhanced Gaussian process regression. (English) Zbl 1477.62238
Frequency principle: Fourier analysis sheds light on deep neural networks. (English) Zbl 1507.68279
MSC:
68T07
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