Deep Neural Network Solution for Finite State Mean Field Game with Error Estimation

被引：2

作者：

Luo, Jialiang ^{[1
]}

Zheng, Harry ^{[1
]}

机构：

[1] Imperial Coll, Dept Math, London SW7 2AZ, England

来源：

DYNAMIC GAMES AND APPLICATIONS | 2023年 / 13卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Finite state mean field game; Forward backward ODE; Deep neural network; Error estimation; ALGORITHM;

D O I：

10.1007/s13235-022-00477-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the numerical solution to a class of continuous time finite state mean field games. We apply the deep neural network (DNN) approach to solving the fully coupled forward and backward ordinary differential equation system that characterizes the equilibrium value function and probability measure of the finite state mean field game. We prove that the error between the true solution and the approximate solution is linear to the square root of DNN loss function. We give an example of applying the DNN method to solve the optimal market making problem with terminal rank-based trading volume reward.

引用

页码：859 / 896

页数：38

共 50 条

[21] State-of-Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Deep Neural Network [J].

Premkumar, M. ;

Sowmya, R. ;

Sridhar, S. ;

Kumar, C. ;

Abbas, Mohamed ;

Alqahtani, Malak S. ;

Nisar, Kottakkaran Sooppy .

CMC-COMPUTERS MATERIALS & CONTINUA, 2022, 73 (03) :6289-6306

[22] State-of-Charge Estimation of Li-ion Battery in Electric Vehicles: A Deep Neural Network Approach [J].

How, Dickson N. T. ;

Hannan, M. A. ;

Lipu, M. S. Hossain ;

Sahari, K. S. M. ;

Ker, P. J. ;

Muttaqi, K. M. .

2019 IEEE INDUSTRY APPLICATIONS SOCIETY ANNUAL MEETING, 2019,

[23] Lithium-ion Battery State of Energy Estimation Using Deep Neural Network and Support Vector Regression [J].

Shrivastava, Prashant ;

Soon, Toy Kok ;

Bin Idris, Mohd Yamani ;

Mekhilef, Saad ;

Adnan, Syed Bahari Ramadzan Syed .

2021 IEEE 12TH ENERGY CONVERSION CONGRESS AND EXPOSITION - ASIA (ECCE ASIA), 2021, :2175-2180

[24] Detection of Driver Fatigue State using Deep Neural Network [J].

Anwar, Noreen ;

Xiong, Gang ;

Guo, Miao ;

Ye, Peijun ;

Ali, Hub ;

Wei, Qinglai .

PROCEEDINGS OF THE 2021 IEEE 16TH CONFERENCE ON INDUSTRIAL ELECTRONICS AND APPLICATIONS (ICIEA 2021), 2021, :79-84

[25] Error Estimation of BFS Extraction With Optimized Neural Network & Frequency Scanning Range [J].

Lv, Tao ;

Ye, Xiaokai ;

Zheng, Yu ;

Ge, Zhiqun ;

Xu, Zhengying ;

Sun, Xiaohan .

JOURNAL OF LIGHTWAVE TECHNOLOGY, 2021, 39 (15) :5149-5155

[26] Neural network guided adjoint computations in dual weighted residual error estimation [J].

Roth, Julian ;

Schroeder, Max ;

Wick, Thomas .

SN APPLIED SCIENCES, 2022, 4 (02)

[27] Error estimation of airborne Strapdown Inertial Navigation System based on neural network [J].

Song, Rui ;

Chen, Xiyuan .

2017 IEEE INTERNATIONAL WORKSHOP ON METROLOGY FOR AEROSPACE (METROAEROSPACE), 2017, :201-205

[28] Deep Scatter Estimation (DSE): Accurate Real-Time Scatter Estimation for X-Ray CT Using a Deep Convolutional Neural Network [J].

Maier, Joscha ;

Sawall, Stefan ;

Knaup, Michael ;

Kachelriess, Marc .

JOURNAL OF NONDESTRUCTIVE EVALUATION, 2018, 37 (03)

[29] Deep Ritz- Finite element methods: Neural network methods trained with finite elements [J].

Grekas, Georgios ;

Makridakis, Charalambos G. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2025, 437

[30] Direction of Arrival Estimation of Array Defects Based on Deep Neural Network [J].

Li, Jianxiong ;

Shao, Xingkai ;

Li, Jie ;

Ge, Lijun .

CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2022, 41 (09) :4906-4927

← 1 2 3 4 5 →