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DGM: A deep learning algorithm for solving partial differential equations

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Cited by:

  1. Jiequn Han & Ruimeng Hu & Jihao Long, 2020. "Convergence of Deep Fictitious Play for Stochastic Differential Games," Papers 2008.05519, arXiv.org, revised Mar 2021.
  2. Fujun Cao & Xiaobin Guo & Fei Gao & Dongfang Yuan, 2023. "Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural Networks," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
  3. Carl Remlinger & Joseph Mikael & Romuald Elie, 2022. "Robust Operator Learning to Solve PDE," Working Papers hal-03599726, HAL.
  4. Cameron Martin & Hongyuan Zhang & Julia Costacurta & Mihai Nica & Adam R Stinchcombe, 2022. "Solving Elliptic Equations with Brownian Motion: Bias Reduction and Temporal Difference Learning," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1603-1626, September.
  5. Daeyung Gim & Hyungbin Park, 2021. "A deep learning algorithm for optimal investment strategies," Papers 2101.12387, arXiv.org.
  6. Kristina O. F. Williams & Benjamin F. Akers, 2023. "Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning," Mathematics, MDPI, vol. 11(13), pages 1-14, June.
  7. Philipp Grohs & Arnulf Jentzen & Diyora Salimova, 2022. "Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms," Partial Differential Equations and Applications, Springer, vol. 3(4), pages 1-41, August.
  8. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," CARF F-Series CARF-F-504, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2022.
  9. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
  10. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
  11. Jialiang Luo & Harry Zheng, 2023. "Deep Neural Network Solution for Finite State Mean Field Game with Error Estimation," Dynamic Games and Applications, Springer, vol. 13(3), pages 859-896, September.
  12. Tianchen Zhao & Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2022. "Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing," Papers 2207.10838, arXiv.org.
  13. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2022. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver (Journal of Computational Physics, published online 19 January 2022)," CARF F-Series CARF-F-532, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2022.
  14. Andrew Na & Justin Wan, 2023. "Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks," Papers 2301.08232, arXiv.org.
  15. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," Papers 2101.09890, arXiv.org, revised Jan 2021.
  16. Zhang, Jincheng & Zhao, Xiaowei, 2021. "Spatiotemporal wind field prediction based on physics-informed deep learning and LIDAR measurements," Applied Energy, Elsevier, vol. 288(C).
  17. Anderson, William & Farazmand, Mohammad, 2024. "Fisher information and shape-morphing modes for solving the Fokker–Planck equation in higher dimensions," Applied Mathematics and Computation, Elsevier, vol. 467(C).
  18. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.
  19. Jiefei Yang & Guanglian Li, 2024. "Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options," Papers 2405.02570, arXiv.org.
  20. Jiang Yu Nguwi & Nicolas Privault, 2023. "A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations," Partial Differential Equations and Applications, Springer, vol. 4(4), pages 1-20, August.
  21. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
  22. Edson Pindza & Jules Clement Mba & Sutene Mwambi & Nneka Umeorah, 2023. "Neural Network for valuing Bitcoin options under jump-diffusion and market sentiment model," Papers 2310.09622, arXiv.org.
  23. Alexandre Pannier & Cristopher Salvi, 2024. "A path-dependent PDE solver based on signature kernels," Papers 2403.11738, arXiv.org.
  24. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
  25. Marlon Azinovic & Luca Gaegauf & Simon Scheidegger, 2022. "Deep Equilibrium Nets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1471-1525, November.
  26. Hajimohammadi, Zeinab & Baharifard, Fatemeh & Ghodsi, Ali & Parand, Kourosh, 2021. "Fractional Chebyshev deep neural network (FCDNN) for solving differential models," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
  27. Li, Jiaheng & Li, Biao, 2022. "Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  28. Weilong Fu & Ali Hirsa, 2022. "Solving barrier options under stochastic volatility using deep learning," Papers 2207.00524, arXiv.org.
  29. Al-Aradi, Ali & Correia, Adolfo & Jardim, Gabriel & de Freitas Naiff, Danilo & Saporito, Yuri, 2022. "Extensions of the deep Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 430(C).
  30. Jentzen, Arnulf & Welti, Timo, 2023. "Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation," Applied Mathematics and Computation, Elsevier, vol. 455(C).
  31. Ian Holloway & Aihua Wood & Alexander Alekseenko, 2021. "Acceleration of Boltzmann Collision Integral Calculation Using Machine Learning," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
  32. William Lefebvre & Gr'egoire Loeper & Huy^en Pham, 2022. "Differential learning methods for solving fully nonlinear PDEs," Papers 2205.09815, arXiv.org.
  33. Peng Zhi & Yuching Wu & Cheng Qi & Tao Zhu & Xiao Wu & Hongyu Wu, 2023. "Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
  34. Konstantinos Prantikos & Lefteri H. Tsoukalas & Alexander Heifetz, 2022. "Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin," Energies, MDPI, vol. 15(20), pages 1-22, October.
  35. Umutoni, Lisa & Samadi, Vidya, 2024. "Application of machine learning approaches in supporting irrigation decision making: A review," Agricultural Water Management, Elsevier, vol. 294(C).
  36. Zhao, Xinyue Evelyn & Hao, Wenrui & Hu, Bei, 2022. "Two neural-network-based methods for solving elliptic obstacle problems," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
  37. Shuaiqiang Liu & Lech A. Grzelak & Cornelis W. Oosterlee, 2022. "The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations," Risks, MDPI, vol. 10(3), pages 1-27, February.
  38. Andrew Papanicolaou & Hao Fu & Prashanth Krishnamurthy & Farshad Khorrami, 2023. "A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization with MGARCH and Small Transaction Costs," Papers 2301.10869, arXiv.org, revised Feb 2023.
  39. Ma, Jie & Yang, Zhiwei & Du, Ning, 2024. "Learning solution of a bond-based linear peridynamic model using LS-SVR method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 262-272.
  40. Jikai Jin & Yiping Lu & Jose Blanchet & Lexing Ying, 2022. "Minimax Optimal Kernel Operator Learning via Multilevel Training," Papers 2209.14430, arXiv.org, revised Jul 2023.
  41. Beatriz Salvador & Cornelis W. Oosterlee & Remco van der Meer, 2020. "Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
  42. Timoth'ee Fabre & Ioane Muni Toke, 2024. "Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets," Papers 2401.09361, arXiv.org, revised Jan 2024.
  43. Laura Leal & Mathieu Lauri`ere & Charles-Albert Lehalle, 2020. "Learning a functional control for high-frequency finance," Papers 2006.09611, arXiv.org, revised Feb 2021.
  44. Dehghani, Hamidreza & Zilian, Andreas, 2021. "A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 398-417.
  45. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Neural Optimal Stopping Boundary," Papers 2205.04595, arXiv.org, revised May 2023.
  46. Sebastian Jaimungal & Yuri F. Saporito & Max O. Souza & Yuri Thamsten, 2023. "Optimal Trading in Automatic Market Makers with Deep Learning," Papers 2304.02180, arXiv.org.
  47. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised May 2024.
  48. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
  49. Ali Al-Aradi & Adolfo Correia & Danilo de Frietas Naiff & Gabriel Jardim & Yuri Saporito, 2019. "Extensions of the Deep Galerkin Method," Papers 1912.01455, arXiv.org, revised Apr 2022.
  50. Quan, Ho Dac & Huynh, Hieu Trung, 2023. "Solving partial differential equation based on extreme learning machine," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 697-708.
  51. Xiangdong Liu & Yu Gu, 2023. "Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
  52. Choi, So Eun & Jang, Hyun Jin & Lee, Kyungsub & Zheng, Harry, 2021. "Optimal market-Making strategies under synchronised order arrivals with deep neural networks," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
  53. Ovadia, Oded & Kahana, Adar & Turkel, Eli, 2024. "A convolutional dispersion relation preserving scheme for the acoustic wave equation," Applied Mathematics and Computation, Elsevier, vol. 461(C).
  54. Li, Yixin & Hu, Xianliang, 2022. "Artificial neural network approximations of Cauchy inverse problem for linear PDEs," Applied Mathematics and Computation, Elsevier, vol. 414(C).
  55. Liyue Wang & Haochen Zhang & Cong Wang & Jun Tao & Xinyue Lan & Gang Sun & Jinzhang Feng, 2024. "A Review of Intelligent Airfoil Aerodynamic Optimization Methods Based on Data-Driven Advanced Models," Mathematics, MDPI, vol. 12(10), pages 1-21, May.
  56. Yangang Chen & Justin W. L. Wan, 2019. "Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions," Papers 1909.11532, arXiv.org.
  57. Yuri F. Saporito & Zhaoyu Zhang, 2020. "PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations," Papers 2003.02035, arXiv.org, revised Apr 2020.
  58. Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2023. "Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations," Papers 2311.12239, arXiv.org.
  59. Huicong Zhong & Xiaobing Feng, 2023. "An Efficient and Fast Sparse Grid Algorithm for High-Dimensional Numerical Integration," Mathematics, MDPI, vol. 11(19), pages 1-26, October.
  60. Zhao Chen & Yang Liu & Hao Sun, 2021. "Physics-informed learning of governing equations from scarce data," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
  61. Olivier Bokanowski & Averil Prost & Xavier Warin, 2023. "Neural networks for first order HJB equations and application to front propagation with obstacle terms," Partial Differential Equations and Applications, Springer, vol. 4(5), pages 1-36, October.
  62. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A New Efficient Approximation Scheme for Solving High-Dimensional Semilinear PDEs: Control Variate Method for Deep BSDE Solver," CIRJE F-Series CIRJE-F-1159, CIRJE, Faculty of Economics, University of Tokyo.
  63. Hainaut, Donatien & Casas, Alex, 2024. "Option pricing in the Heston model with Physics inspired neural networks," LIDAM Discussion Papers ISBA 2024002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  64. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
  65. Ruimeng Hu & Quyuan Lin & Alan Raydan & Sui Tang, 2023. "Higher-order error estimates for physics-informed neural networks approximating the primitive equations," Partial Differential Equations and Applications, Springer, vol. 4(4), pages 1-35, August.
  66. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.
  67. Yuga Iguchi & Riu Naito & Yusuke Okano & Akihiko Takahashi & Toshihiro Yamada, 2021. "Deep Asymptotic Expansion: Application to Financial Mathematics," CIRJE F-Series CIRJE-F-1178, CIRJE, Faculty of Economics, University of Tokyo.
  68. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.
  69. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.
  70. Mingcan Wang & Xiangjun Wang, 2024. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 12(7), pages 1-22, April.
  71. Kathrin Glau & Linus Wunderlich, 2020. "The Deep Parametric PDE Method: Application to Option Pricing," Papers 2012.06211, arXiv.org.
  72. Stefan Kremsner & Alexander Steinicke & Michaela Szolgyenyi, 2020. "A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics," Papers 2010.15757, arXiv.org, revised Dec 2020.
  73. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2023. "Deep stochastic optimization in finance," Digital Finance, Springer, vol. 5(1), pages 91-111, March.
  74. Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
  75. Ariel Neufeld & Philipp Schmocker & Sizhou Wu, 2024. "Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity," Papers 2405.05192, arXiv.org.
  76. Anders Max Reppen & Halil Mete Soner, 2023. "Deep empirical risk minimization in finance: Looking into the future," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 116-145, January.
  77. Emmanuil H. Georgoulis & Antonis Papapantoleon & Costas Smaragdakis, 2024. "A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models," Papers 2401.06740, arXiv.org.
  78. Lukas Gonon, 2021. "Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality," Papers 2106.08900, arXiv.org.
  79. Ying Li & Longxiang Xu & Shihui Ying, 2022. "DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-35, June.
  80. Kevin Shuai Zhang & Traian Pirvu, 2021. "Pricing spread option with liquidity adjustments," Papers 2101.00223, arXiv.org.
  81. Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse & Tuan Anh Nguyen, 2020. "A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-34, April.
  82. Christian Bayer & Blanka Horvath & Aitor Muguruza & Benjamin Stemper & Mehdi Tomas, 2019. "On deep calibration of (rough) stochastic volatility models," Papers 1908.08806, arXiv.org.
  83. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
  84. Jingruo Sun, 2022. "Deep Galerkin Method for Mean Field Control Problem," Papers 2212.01719, arXiv.org, revised Feb 2024.
  85. Ashish Dhiman & Yibei Hu, 2023. "Physics Informed Neural Network for Option Pricing," Papers 2312.06711, arXiv.org.
  86. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.
  87. Assouli, Mouhcine & Missaoui, Badr, 2023. "Deep learning for Mean Field Games with non-separable Hamiltonians," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  88. Yubiao Sun & Qiankun Sun & Kan Qin, 2021. "Physics-Based Deep Learning for Flow Problems," Energies, MDPI, vol. 14(22), pages 1-24, November.
  89. William Lefebvre & Enzo Miller, 2021. "Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 134-168, October.
  90. William Lefebvre & Grégoire Loeper & Huyên Pham, 2023. "Differential learning methods for solving fully nonlinear PDEs," Digital Finance, Springer, vol. 5(1), pages 183-229, March.
  91. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2020. "Pricing and Hedging American-Style Options with Deep Learning," JRFM, MDPI, vol. 13(7), pages 1-12, July.
  92. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
  93. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.
  94. Alessandro Gnoatto & Marco Patacca & Athena Picarelli, 2022. "A deep solver for BSDEs with jumps," Papers 2211.04349, arXiv.org.
  95. Ali Al-Aradi & Adolfo Correia & Danilo Naiff & Gabriel Jardim & Yuri Saporito, 2018. "Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning," Papers 1811.08782, arXiv.org.
  96. Huyên Pham & Xavier Warin & Maximilien Germain, 2021. "Neural networks-based backward scheme for fully nonlinear PDEs," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-24, February.
  97. Xi’an Li & Jinran Wu & Lei Zhang & Xin Tai, 2022. "Solving a Class of High-Order Elliptic PDEs Using Deep Neural Networks Based on Its Coupled Scheme," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
  98. Liao, Guangyuan & Zhang, Limin, 2022. "Solving flows of dynamical systems by deep neural networks and a novel deep learning algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 331-342.
  99. Chaofan Sun & Ken Seng Tan & Wei Wei, 2022. "Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms," Papers 2201.09105, arXiv.org, revised Jan 2022.
  100. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
  101. García, P., 2022. "Modeling systems with machine learning based differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
  102. Yuga Iguchi & Riu Naito & Yusuke Okano & Akihiko Takahashi & Toshihiro Yamada, 2021. "Deep Asymptotic Expansion with Weak Approximation ," CIRJE F-Series CIRJE-F-1168, CIRJE, Faculty of Economics, University of Tokyo.
  103. Salah A. Faroughi & Ramin Soltanmohammadi & Pingki Datta & Seyed Kourosh Mahjour & Shirko Faroughi, 2023. "Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
  104. Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012, arXiv.org, revised Dec 2020.
  105. José Alberto Rodrigues, 2024. "Using Physics-Informed Neural Networks (PINNs) for Tumor Cell Growth Modeling," Mathematics, MDPI, vol. 12(8), pages 1-9, April.
  106. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2022. "Deep learning and American options via free boundary framework," Papers 2211.11803, arXiv.org, revised Dec 2022.
  107. Runlin Zhang & Nuo Xu & Kai Zhang & Lei Wang & Gui Lu, 2023. "A Parametric Physics-Informed Deep Learning Method for Probabilistic Design of Thermal Protection Systems," Energies, MDPI, vol. 16(9), pages 1-20, April.
  108. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
  109. Yue, Jing & Li, Jian, 2023. "Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems," Applied Mathematics and Computation, Elsevier, vol. 437(C).
  110. Yuga Iguchi & Riu Naito & Yusuke Okano & Akihiko Takahashi & Toshihiro Yamada, 2021. "Deep Asymptotic Expansion: Application to Financial Mathematics（forthcoming in proceedings of IEEE CSDE 2021)," CARF F-Series CARF-F-523, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  111. Rudiger Frey & Verena Kock, 2021. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Papers 2109.11403, arXiv.org, revised Sep 2021.
  112. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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