| Abstract: |
| We introduce a machine-learning-based approach for constructing a continuum non-Newtonian fluid dynamics model directly from a micro-scale description. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from a generalized extendable energy functional structure, and be learned from the micro-scale model with clear physical interpretation. The final model, named the deep non-Newtonian model (DeePN$^2$), takes the form of conventional non-Newtonian fluid dynamics models and ensures energy stability. Numerical results demonstrate the accuracy and robustness of DeePN$^2$. |
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