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Artificial intelligence and deep learning methods for solving differential equations: the state of the art and prospects
- Chinese Journal of Intelligent Science and Technology Vol. 4, Issue 4, Pages: 461-476(2022)
- 作者机构：
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
- 作者简介：
- 基金信息：
DOI：10.11959/j.issn.2096-6652.202255
CLC： TP18-
Published Online：2022-12，
Published：15 December 2022
- 稿件说明：
移动端阅览
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.
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. DOI： 10.11959/j.issn.2096-6652.202255.
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。
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.
关键词
Keywords
references
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