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We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks.
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Neural-network methods for boundary value problems with irregular boundaries,
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Large scale multiple kernel learning,
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SimpleMKL,
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SPF-GMKL: generalized multiple kernel learning with a million kernels,
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EasyMKL: a scalable multiple kernel learning algorithm,
F. Aiolli, M. Donini, · 2014
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A geometric algorithm for scalable multiple kernel learning,
J. Moeller, P. Raman, S. Venkatasubramanian, A. Saha, · 2014
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The numerical solution of Fokker-Planck equation with radial basis functions (RBFs) based on the meshless technique of Kansa’s approach and Galerkin method,
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Steady states of Fokker-Planck equations: I. Existence,
W. Huang, M. Ji, Z. Liu, Y. Yi, · 2015
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations,
J. Han, A. Jentzen, et al., · 2017
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Deep primal-dual algorithm for bsdes: Applications of machine learning to cva and im,
P. Henry-Labordere, · 2017
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Solving high-dimensional partial differential equations using deep learning,
J. Han, A. Jentzen, W. E, · 2018
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M. Raissi, · 2018
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Hybrid Gaussian-cubic radial basis functions for scattered data interpolation,
P. K. Mishra, S. K. Nath, M. K. Sen, G. E. Fasshauer, · 2018
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A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels,
P. K. Mishra, G. E. Fasshauer, M. K. Sen, L. Ling, · 2018
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A new support vector machine with an optimal additive kernel,
J. Baek, E. Kim, · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2019
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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations,
C. Beck, W. E, A. Jentzen, · 2019
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Machine learning for semi-linear PDEs,
Q. Chan-Wai-Nam, J. Mikael, X. Warin, · 2019
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A deep learning method for solving Fokker-Planck equations,
J. Zhai, M. Dobson, Y. Li, · 2022
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Separable pinn: Mitigating the curse of dimensionality in physics-informed neural networks,
J. Cho, S. Nam, H. Yang, S.-B. Yun, Y. Hong, E. Park, · 2022
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H. Zhang, R. Zhang, T. Zhou, · 2022
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Adaptive deep density approximation for Fokker-Planck equations,
K. Tang, X. Wan, Q. Liao, · 2022
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Numerical solution of the Fokker-Planck equation using physics-based mixture models,
A. Tabandeh, N. Sharma, L. Iannacone, P. Gardoni, · 2022
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Kernel flows: from learning kernels from data into the abyss,
H. Owhadi, G. R. Yoo, · 2019
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Kernel flows: From learning kernels from data into the abyss,
H. Owhadi, G. R. Yoo, · 2019
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Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations,
C. Beck, F. Hornung, M. Hutzenthaler, A. Jentzen, T. Kruse, · 2020
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Deep backward schemes for high-dimensional nonlinear PDEs,
C. Huré, H. Pham, X. Warin, · 2020
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Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations,
M. Hutzenthaler, A. Jentzen, T. Kruse, T. Anh Nguyen, P. von Wurstemberger, · 2020
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Three algorithms for solving high-dimensional fully coupled FBSDEs through deep learning,
S. Ji, S. Peng, Y. Peng, X. Zhang, · 2020
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Learning dynamical systems from data: a simple cross-validation perspective, part I: Parametric kernel flows,
B. Hamzi, H. Owhadi, · 2020
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Computing the invariant distribution of randomly perturbed dynamical systems using deep learning,
B. Lin, Q. Li, W. Ren, · 2022
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Computing high-dimensional invariant distributions from noisy data,
B. Lin, Q. Li, W. Ren, · 2022
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Learning “best" kernels from data in Gaussian process regression. with application to aerodynamics,
J.-L. Akian, L. Bonnet, H. Owhadi, E. Savin, · 2022
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Fourierformer: Transformer meets generalized Fourier integral theorem,
T. M. Nguyen, M. Pham, T. M. Nguyen, K. Nguyen, S. Osher, N. Ho, · 2022
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V. I. Bogachev, N. V. Krylov, M. Röckner, S. V. Shaposhnikov, Fokker–Planck–Kolmogorov Equations, volume 207, American Mathematical Society, 2022
2022
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H. Alhussein, M. Khasawneh, M. F. Daqaq, · 2023
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Deep learning framework for solving Fokker-Planck equations with low-rank separation representation,
H. Zhang, Y. Xu, Q. Liu, Y. Li, · 2023
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Learning physics-informed neural networks without stacked back-propagation,
D. He, S. Li, W. Shi, X. Gao, J. Zhang, J. Bian, L. Wang, T.-Y. Liu, · 2023
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Tackling the curse of dimensionality with physics-informed neural networks,
Z. Hu, K. Shukla, G. E. Karniadakis, K. Kawaguchi, · 2023
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Probability flow solution of the Fokker-Planck equation,
N. M. Boffi, E. Vanden-Eijnden, · 2023
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Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions,
W. Anderson, M. Farazmand, · 2023
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Artificial neural network solver for time-dependent Fokker-Planck equations,
Y. Li, C. Meredith, · 2023
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Learning zeros of Fokker-Planck operators,
P. Mandal, A. Apte, · 2023
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Stationary density estimation of Itô diffusions using deep learning,
Y. Gu, J. Harlim, S. Liang, H. Yang, · 2023
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Radial basis function neural networks solution for stationary probability density function of nonlinear stochastic systems,
X. Wang, J. Jiang, L. Hong, A. Zhao, J.-Q. Sun, · 2023
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Symbolic discovery of optimization algorithms,
X. Chen, C. Liang, D. Huang, E. Real, K. Wang, H. Pham, X. Dong, T. Luong, C.-J. Hsieh, Y. Lu, et al., · 2024
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Learning dynamical systems from data: A simple cross-validation perspective, part v: Sparse kernel flows for 132 chaotic dynamical systems,
L. Yang, X. Sun, B. Hamzi, H. Owhadi, N. Xie, · 2024
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