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DGM: A deep learning algorithm for solving partial differential equations

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Cited by:

  1. 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.
  2. Benjamin F. Akers & Kristina O. F. Williams, 2024. "Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning," Mathematics, MDPI, vol. 12(17), pages 1-10, September.
  3. Jiequn Han & Ruimeng Hu & Jihao Long, 2020. "Convergence of Deep Fictitious Play for Stochastic Differential Games," Papers 2008.05519, arXiv.org, revised Mar 2021.
  4. Riu Naito & Toshihiro Yamada, 2024. "Deep Kusuoka Approximation: High-Order Spatial Approximation for Solving High-Dimensional Kolmogorov Equations and Its Application to Finance," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1443-1461, September.
  5. 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.
  6. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.
  7. 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.
  8. 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.
  9. Christian Bayer & Blanka Horvath & Aitor Muguruza & Benjamin Stemper & Mehdi Tomas, 2019. "On deep calibration of (rough) stochastic volatility models," Papers 1908.08806, arXiv.org.
  10. William Lefebvre & Gr'egoire Loeper & Huy^en Pham, 2022. "Differential learning methods for solving fully nonlinear PDEs," Papers 2205.09815, arXiv.org.
  11. 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.
  12. Hainaut, Donatien & Vrins, Frédéric, 2024. "European option pricing with model constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2024021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  13. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
  14. Riu Naito & Toshihiro Yamada, 2024. "Deep high-order splitting method for semilinear degenerate PDEs and application to high-dimensional nonlinear pricing models," Digital Finance, Springer, vol. 6(4), pages 693-725, December.
  15. 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.
  16. 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.
  17. 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.
  18. Kristoffer Andersson & Alessandro Gnoatto & Marco Patacca & Athena Picarelli, 2022. "A deep solver for BSDEs with jumps," Papers 2211.04349, arXiv.org, revised Nov 2024.
  19. Carl Remlinger & Joseph Mikael & Romuald Elie, 2022. "Robust Operator Learning to Solve PDE," Working Papers hal-03599726, HAL.
  20. 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.
  21. Alexandre Pannier & Cristopher Salvi, 2024. "A path-dependent PDE solver based on signature kernels," Papers 2403.11738, arXiv.org, revised Oct 2024.
  22. 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).
  23. 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.
  24. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
  25. Donatien Hainaut & Alex Casas, 2024. "Option pricing in the Heston model with physics inspired neural networks," Annals of Finance, Springer, vol. 20(3), pages 353-376, September.
  26. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
  27. Dupret, Jean-Loup & Hainaut, Donatien, 2024. "Deep learning for high-dimensional continuous-time stochastic optimal control without explicit solution," LIDAM Discussion Papers ISBA 2024016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  28. Christian Beck & Lukas Gonon & Arnulf Jentzen, 2024. "Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations," Partial Differential Equations and Applications, Springer, vol. 5(6), pages 1-47, December.
  29. 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.
  30. Umutoni, Lisa & Samadi, Vidya, 2024. "Application of machine learning approaches in supporting irrigation decision making: A review," Agricultural Water Management, Elsevier, vol. 294(C).
  31. 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.
  32. Zhouzhou Gu & Mathieu Lauri`ere & Sebastian Merkel & Jonathan Payne, 2024. "Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models," Papers 2406.13726, arXiv.org.
  33. 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.
  34. She, Ruifeng & Ouyang, Yanfeng, 2024. "Hybrid truck–drone delivery under aerial traffic congestion," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
  35. 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).
  36. Jingruo Sun, 2022. "Deep Galerkin Method for Mean Field Control Problem," Papers 2212.01719, arXiv.org, revised Feb 2024.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. Jésus Fernández-Villaverde & Galo Nuño & Jesse Perla & Jesús Fernández-Villaverde, 2024. "Taming the Curse of Dimensionality: Quantitative Economics with Deep Learning," CESifo Working Paper Series 11448, CESifo.
  42. 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.
  43. 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.
  44. Ashish Dhiman & Yibei Hu, 2023. "Physics Informed Neural Network for Option Pricing," Papers 2312.06711, arXiv.org.
  45. Lukas Gonon, 2024. "Deep neural network expressivity for optimal stopping problems," Finance and Stochastics, Springer, vol. 28(3), pages 865-910, July.
  46. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2024. "Deep Learning and American Options via Free Boundary Framework," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 979-1022, August.
  47. Rubén Darío Ortiz Ortiz & Oscar Martínez Núñez & Ana Magnolia Marín Ramírez, 2024. "Solving Viscous Burgers’ Equation: Hybrid Approach Combining Boundary Layer Theory and Physics-Informed Neural Networks," Mathematics, MDPI, vol. 12(21), pages 1-30, November.
  48. 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.
  49. 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.
  50. Andrew Na & Justin Wan, 2023. "Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks," Papers 2301.08232, arXiv.org.
  51. 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.
  52. 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.
  53. Talbi, Mehdi, 2024. "A finite-dimensional approximation for partial differential equations on Wasserstein space," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
  54. 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.
  55. 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.
  56. 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.
  57. Daeyung Gim & Hyungbin Park, 2021. "A deep learning algorithm for optimal investment strategies," Papers 2101.12387, arXiv.org.
  58. Chen, Xingyu & Cen, Jianhuan & Zou, Qingsong, 2024. "Adaptive trajectories sampling for solving PDEs with deep learning methods," Applied Mathematics and Computation, Elsevier, vol. 481(C).
  59. 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.
  60. 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).
  61. 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.
  62. 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.
  63. 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).
  64. 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.
  65. 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.
  66. 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).
  67. Zhang, Jincheng & Zhao, Xiaowei, 2021. "Spatiotemporal wind field prediction based on physics-informed deep learning and LIDAR measurements," Applied Energy, Elsevier, vol. 288(C).
  68. 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).
  69. 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.
  70. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.
  71. 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.
  72. 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.
  73. 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.
  74. 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.
  75. 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.
  76. 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 Nov 2024.
  77. García, P., 2022. "Modeling systems with machine learning based differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
  78. Assouli, Mouhcine & Missaoui, Badr, 2024. "Deep Policy Iteration for high-dimensional mean field games," Applied Mathematics and Computation, Elsevier, vol. 481(C).
  79. Assouli, Mouhcine & Missaoui, Badr, 2023. "Deep learning for Mean Field Games with non-separable Hamiltonians," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
  80. 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.
  81. Yubiao Sun & Qiankun Sun & Kan Qin, 2021. "Physics-Based Deep Learning for Flow Problems," Energies, MDPI, vol. 14(22), pages 1-24, November.
  82. 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.
  83. 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.
  84. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Neural Optimal Stopping Boundary," Papers 2205.04595, arXiv.org, revised May 2023.
  85. Jiefei Yang & Guanglian Li, 2024. "Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options," Papers 2405.02570, arXiv.org.
  86. Jingtang Ma & Shan Yang, 2024. "High-dimensional stochastic control models for newsvendor problems and deep learning resolution," Annals of Operations Research, Springer, vol. 339(1), pages 789-811, August.
  87. Hyeong-Ohk Bae & Seunggu Kang & Muhyun Lee, 2024. "Option Pricing and Local Volatility Surface by Physics-Informed Neural Network," Computational Economics, Springer;Society for Computational Economics, vol. 64(5), pages 3143-3159, November.
  88. 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.
  89. Weilong Fu & Ali Hirsa, 2022. "Solving barrier options under stochastic volatility using deep learning," Papers 2207.00524, arXiv.org.
  90. 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.
  91. Kathrin Glau & Linus Wunderlich, 2020. "The Deep Parametric PDE Method: Application to Option Pricing," Papers 2012.06211, arXiv.org.
  92. 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.
  93. 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).
  94. Alberto Gennaro & Thibaut Mastrolia, 2024. "Delegated portfolio management with random default," Papers 2410.13103, arXiv.org.
  95. 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.
  96. Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012, arXiv.org, revised Dec 2020.
  97. 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).
  98. 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.
  99. 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.
  100. 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.
  101. 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.
  102. Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
  103. 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.
  104. José Alberto Rodrigues, 2024. "Using Physics-Informed Neural Networks (PINNs) for Tumor Cell Growth Modeling," Mathematics, MDPI, vol. 12(8), pages 1-9, April.
  105. Ariel Neufeld & Philipp Schmocker & Sizhou Wu, 2024. "Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs," Papers 2405.05192, arXiv.org, revised Jan 2025.
  106. 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.
  107. Li, Yixin & Hu, Xianliang, 2022. "Artificial neural network approximations of Cauchy inverse problem for linear PDEs," Applied Mathematics and Computation, Elsevier, vol. 414(C).
  108. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
  109. 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.
  110. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
  111. 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.
  112. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
  113. 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).
  114. Wang, Xinyu & Zhang, Yuxing & Zhang, Shuhua, 2024. "Dynamic order allocation in a duopoly hybrid workforce of competition: A machine learning approach," European Journal of Operational Research, Elsevier, vol. 315(2), pages 668-690.
  115. Maxim Bichuch & Jiahao Hou, 2024. "Deep PDE solution to BSDE," Digital Finance, Springer, vol. 6(4), pages 727-758, December.
  116. 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.
  117. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised Sep 2024.
  118. 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.
  119. 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.
  120. 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.
  121. 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.
  122. 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).
  123. 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.
  124. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
  125. 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.
  126. Lukas Gonon, 2021. "Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality," Papers 2106.08900, arXiv.org.
  127. Gero Junike & Hauke Stier, 2024. "Enhancing Fourier pricing with machine learning," Papers 2412.05070, arXiv.org.
  128. 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.
  129. 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.
  130. 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).
  131. Kevin Shuai Zhang & Traian Pirvu, 2021. "Pricing spread option with liquidity adjustments," Papers 2101.00223, arXiv.org.
  132. 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.
  133. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
  134. Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2023. "Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations," Papers 2311.12239, arXiv.org.
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