Reproduce “Unsupervised operator learning approach for dissipative equations via Onsager principle” on OpenResearch

About this paper

Zhipeng Chang, Zhenye Wen, Xiaofei Zhao

The Deep Onsager Operator Learning (DOOL) method introduces an unsupervised framework for learning operators of dissipative equations by leveraging the Onsager Variational Principle as a loss function. It accurately predicts system dynamics and fluxes for various PDEs without labeled data, demonstrating superior temporal extrapolation and enhanced generalization compared to supervised operator learning approaches.

Key insights

• The Onsager Variational Principle provides a physically grounded, unsupervised objective function, eliminating the need for labeled data by directly minimizing a functional related to system dynamics.
• Decoupling spatial and temporal components during training allows the operator network to learn instantaneous constitutive relations, leading to more efficient training and robust temporal extrapolation.
• Learning the flux or rate of change, rather than the state itself, enables an explicit time-stepping scheme for evolving the system, thereby extending predictions beyond trained time intervals.

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