求解微分方程的人工智能与深度学习方法：现状及展望

doi:10.11959/j.issn.2096-6652.202255

智能科学与技术学报 ›› 2022, Vol. 4 ›› Issue (4): 461-476.doi: 10.11959/j.issn.2096-6652.202255

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求解微分方程的人工智能与深度学习方法：现状及展望

卢经纬¹^,², 程相¹^,³, 王飞跃¹^,³

¹ 中国科学院自动化研究所复杂系统管理与控制国家重点实验室，北京 100190
² 青岛智能产业技术研究院，山东青岛 266114
³ 中国科学院大学人工智能学院，北京 100049

修回日期:2022-11-18 出版日期:2022-12-15 发布日期:2022-12-01
作者简介:卢经纬（1990- ），男，青岛智能产业技术研究院助理研究员，主要研究方向为最优控制、平行控制、自适应动态规划和深度强化学习
程相（1994- ），男，中国科学院自动化研究所博士生，主要研究方向为智慧油田、深度学习和平行控制
王飞跃（1961- ），男，中国科学院自动化研究所复杂系统管理与控制国家重点实验室主任，主要研究方向为平行系统的方法与应用、社会计算、平行智能以及知识自动化
基金资助:
国家自然科学基金资助项目(U1811463);行动元联合研究项目伺服驱动系统建模、决策和控制算法研究

Artificial intelligence and deep learning methods for solving differential equations: the state of the art and prospects

Jingwei LU¹^,², Xiang CHENG¹^,³, Fei-Yue WANG¹^,³

¹ The State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
² Qingdao Academy of Intelligent Industries, Qingdao 266114, China
³ School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China

Revised:2022-11-18 Online:2022-12-15 Published:2022-12-01
Supported by:
The National Natural Science Foundation of China(U1811463);Motion G, Inc.Collaborative Research Project for Modeling, Decision and Control Algorithms of Servo Drive Systems

摘要/Abstract

摘要：

随着基础理论和硬件计算能力的飞速发展，深度学习技术在众多领域取得了令人瞩目的成绩。作为描述客观物理世界的重要工具，长期以来微分方程是各领域研究人员关心的重点。近年来，深度学习和微分方程的结合逐渐成了研究的热点。由于深度学习能够从大量数据中高效地提取特征，微分方程能够反应客观的物理规律，因此二者的结合可以有效地提升深度学习的泛化性，同时增强深度学习的可解释性。首先，介绍了深度学习求解微分方程的基本问题。其次，介绍了两类深度学习求解微分方程的方法：数据驱动和物理知情方法。然后，讨论了微分方程深度学习求解方法在实际中的应用。与此同时，在充分调研的基础上提出了科学智能大模型——DeDAO（微分之道），以应对现有的挑战。最后，对微分方程深度学习求解方法进行了简要总结。

关键词: 人工智能, 深度学习, 神经网络, 微分方程

Abstract:

With the rapid advancement of fundamental theories and computing capacity, deep learning techniques have made impressive achievements in many fields.Differential equations, as an important tool for describing the physical world, have long been a focus of interest for researchers in various fields.Combining the two methods has gained popularity as a study issue in recent years.Since deep learning can efficiently extract features from large amounts of data and differential equations can reflect objective physical laws, the combination of the two can effectively improve the generalization ability of deep learning and enhance the interpretability of deep learning.Firstly, the problem of solving differential equations by deep learning was briefly introduced.Then, two types of deep learning methods for solving differential equations were introduced: data-driven and physical-informed methods.Furthermore, the applications of relevant deep learning-based solving methods were discussed.Meanwhile, DeDAO (differential equations DAO), a foundation model for artificial intelligence for science, was proposed to address existing challenges.Finally, conclusions of deep learning methods for solving differential equations were presented.

Key words: artificial intelligence, deep learning, neural network, differential equation

中图分类号:

TP18

卢经纬,程相,王飞跃. 求解微分方程的人工智能与深度学习方法：现状及展望[J]. 智能科学与技术学报, 2022, 4(4): 461-476.

Jingwei LU,Xiang CHENG,Fei-Yue WANG. Artificial intelligence and deep learning methods for solving differential equations: the state of the art and prospects[J]. Chinese Journal of Intelligent Science and Technology, 2022, 4(4): 461-476.

图/表 5

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求解微分方程的人工智能与深度学习方法：现状及展望

Artificial intelligence and deep learning methods for solving differential equations: the state of the art and prospects

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