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In this paper we present an adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P) equations.
M. Dobson, Y. Li, J. Zhai, An efficient data-driven solver for Fokker-Planck equations: Algorithm and analysis (2019) · 1906
Earlier work this paper cites.
H. Risken, Fokker-Planck-Kolmogorov equation, Springer, 1984
1984
Earlier work this paper cites.
G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems 2 (4) (1989) 303–314
1989
Earlier work this paper cites.
B. Spencer, L. Bergman, On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems, Nonlinear Dynamics 4 (4) (1993) 357–372
1993
Earlier work this paper cites.
M. Leshno, V. Y. Lin, A. Pinkus, S. Schocken, Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural Networks 6 (6) (1993) 861–867
1993
Earlier work this paper cites.
R. Vilalta, Y. Drissi, A perspective view and survey of meta-learning, Artificial Intelligence Review 18 (2001) 77–95
2001
Earlier work this paper cites.
D. Xiu, J. S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM Journal on Scientific Computing 27 (3) (2005) 1118–1139
2005
Earlier work this paper cites.
I. Babuška, F. Nobile, R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM Journal on Numerical Analysis 45 (3) (2007) 1005–1034
2007
Earlier work this paper cites.
X. Chen, L. Yang, J. Duan, G. E. Karniadakis, Solving inverse stochastic problems from discrete particle observations using the Fokker-Planck equation and physics-informed neural networks (2020) · 2008
Earlier work this paper cites.
J. Foo, X. Wan, G. E. Karniadakis, The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications, Journal of Computational Physics 227 (22) (2008) 9572–9595
2008
Earlier work this paper cites.
X. Ma, N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, Journal of Computational Physics 228 (8) (2009) 3084–3113
2009
Earlier work this paper cites.
P. Ren, Y. Xiao, X. Cheang, P.-Y. Huang, Z. Li, X. Chen, X. Wang, A survey of deep active learning (2020) · 2009
Earlier work this paper cites.
D. Xiu, Numerical methods for stochastic computations: A spectral method approach, Princeton university press, 2010
2010
Earlier work this paper cites.
G. Carlier, A. Galichon, F. Santambrogio, From Knothe’s transport to Brenier’s map and a continuation method for optimal transport, SIAM Journal on Mathematical Analysis 41 (6) (2010) 2554–2576
2010
Earlier work this paper cites.
X. Glorot, Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, in: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010, pp. 249–256
2010
Earlier work this paper cites.
S. Jin, B. Yan, A class of asymptotic-preserving schemes for the Fokker–Planck–Landau equation, Journal of Computational Physics 230 (2011) 6420–6437
2011
Earlier work this paper cites.
X. Glorot, A. Bordes, Y. Bengio, Deep sparse rectifier neural networks, in: Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, 2011, pp. 315–323
2011
Earlier work this paper cites.
S. Dong, Z. Li, Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations (2020) · 2012
Earlier work this paper cites.
A. Narayan, D. Xiu, Stochastic collocation methods on unstructured grids in high dimensions via interpolation, SIAM Journal on Scientific Computing 34 (3) (2012) A1729–A1752
2012
Cited alongside, same era.
H. C. Elman, D. J. Silvester, A. J. Wathen, Finite elements and fast iterative solvers: With applications in incompressible fluid dynamics, Oxford University Press, USA, 2014
2014
Cited alongside, same era.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, Generative adversarial nets, in: Advances in Neural Information Processing Systems, 2014, pp. 2672–2680
2014
Cited alongside, same era.
D. P. Kingma, M. Welling, Auto-Encoding Variational Bayes, stat 1050 (2014) 1
2014
Cited alongside, same era.
G. A. Pavliotis, Stochastic processes and applications: Diffusion processes, the Fokker-Planck and Langevin equations, Vol. 60, Springer, 2014
T. Q. Chen, Y. Rubanova, J. Bettencourt, D. K. Duvenaud, Neural ordinary differential equations, in: Advances in Neural Information Processing Systems, 2018, pp. 6571–6583
2018
Later among the works it cites.
L. Bottou, F. E. Curtis, J. Nocedal, Optimization methods for large-scale machine learning, SIAM Review 60 (2) (2018) 223–311
2018
Later among the works it cites.
Y. Li, A data-driven method for the steady state of randomly perturbed dynamics, Communications in Mathematical Sciences 17 (2019) 1045–1059
2019
Later among the works it cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics 378 (2019) 686–707
2019
Later among the works it cites.
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2014
Cited alongside, same era.
D. P. Kingma, J. Ba, Adam: A method for stochastic optimization (2014) · 2014
Cited alongside, same era.
H. Lei, X. Yang, B. Zheng, G. Lin, N. A. Baker, Constructing surrogate models of complex systems with enhanced sparsity: quantifying the influence of conformational uncertainty in biomolecular solvation, Multiscale Modeling & Simulation 13 (4) (2015) 1327–1353
2015
Cited alongside, same era.
D. W. Scott, Multivariate density estimation: theory, practice, and visualization, John Wiley & Sons, 2015
2015
Cited alongside, same era.
S. Ioffe, C. Szegedy, Batch normalization: Accelerating deep network training by reducing internal covariate shift (2015) · 2015
Cited alongside, same era.
L. Dinh, J. Sohl-Dickstein, S. Bengio, Density estimation using real NVP (2016) · 2016
Cited alongside, same era.
K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, pp. 770–778
2016
Cited alongside, same era.
W. E, A proposal on machine learning via dynamical systems, Communications in Mathematics and Statistics 5 (1) (2017) 1–11
2017
Cited alongside, same era.
2019
Later among the works it cites.
Y. Zhu, N. Zabaras, P.-S. Koutsourelakis, P. Perdikaris, Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data, Journal of Computational Physics 394 (2019) 56–81
2019
Later among the works it cites.
K. Wu, D. Xiu, Numerical aspects for approximating governing equations using data, Journal of Computational Physics 384 (2019) 200–221
2019
Later among the works it cites.
R. Cang, H. Yao, Y. Ren, One-shot generation of near-optimal topology through theory-driven machine learning, Computer-Aid Design 109 (2019) 12–21
2019
Later among the works it cites.
K. Wu, T. Qin, D. Xiu, Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data, SIAM Journal on Scientific Computing 42 (6) (2020) A3704–A3729
2020
Later among the works it cites.
K. Li, K. Tang, T. Wu, Q. Liao, D3M: A deep domain decomposition method for partial differential equations, IEEE Access 8 (2020) 5283–5294
2020
Later among the works it cites.
A. D. Jagtap, E. Kharazmi, G. E. Karniadakis, Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems, Computer Methods in Applied Mechanics and Engineering 365 (2020) 113028
2020
Later among the works it cites.
W. Li, X. Xiang, Y. Xu, Deep domain decomposition method: Elliptic problems, in: J. Lu, R. Ward (Eds.), Proceedings of The First Mathematical and Scientific Machine Learning Conference, Vol. 107 of Proceedings of Machine Learning Research, PMLR, Princeton University, Princeton, NJ, USA, 2020, pp. 269–286
2020
Later among the works it cites.
A. Heinlein, A. Klawonn, M. Lanser, J. Weber, Combining machine learning and domain decomposition methods—a review, Technical report, Universität zu Köln (October 2020)
2020
Later among the works it cites.
H. Sheng, C. Yang, PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries, Journal of Computational Physics (2020) 110085
2020
Later among the works it cites.
X. Wan, S. Wei, Coupling the reduced-order model and the generative model for an importance sampling estimator, Journal of Computational Physics 408 (2020) 109281
2020
Later among the works it cites.
K. Tang, X. Wan, Q. Liao, Deep density estimation via invertible block-triangular mapping, Theoretical & Applied Mechanics Letters 10 (2020) 143
2020
Later among the works it cites.
E. Kharazmi, Z. Zhang, G. E. Karniadakis, hp-VPINNs: Variational physics-informed neural networks with domain decomposition, Computer Methods in Applied Mechanics and Engineering 374 (2021) 113547
2021
Closest in time.
H. Gao, L. Sun, J.-X. Wang, Phygeonet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain, Journal of Computational Physics 428 (2021) 110079
2021
Closest in time.