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AI paradigm for solving differential equations: first-principles data generation and scale-dilation operator AI solver
Xiangshu Gong, Zhiqiang Xie, Xiaowei Jin +4
Many problems are governed by differential equations (DEs). Artificial intelligence (AI) is a new path for solving DEs. However, data is very scarce and existing AI solvers struggl…
Physics Consistency and Latent Dynamics in Spatiotemporal Physics Field Generation
Peimian Du, Jiabin Liu, Xiaowei Jin +2
Data-driven models for spatiotemporal physical field generation, such as flow and acoustic fields, often deviate from governing equations and lack interpretability in latent tempor…
An invariance constrained deep learning network for PDE discovery
Chao Chen, Hui Li, Xiaowei Jin
The discovery of partial differential equations (PDEs) from datasets has attracted increased attention. However, the discovery of governing equations from sparse data with high noi…
Discovering Governing Equations by Machine Learning implemented with Invariance
Chao Chen, Xiaowei Jin, Hui Li
The partial differential equation (PDE) plays a significantly important role in many fields of science and engineering. The conventional case of the derivation of PDE mainly relies…
General solutions for nonlinear differential equations: a rule-based self-learning approach using deep reinforcement learning
Shiyin Wei, Xiaowei Jin, Hui Li
A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial…