One essential challenge in the computational modeling of multiscale systems is the availability of reliable and interpretable closures that faithfully encode the micro-dynamics. For systems without clear scale separation, there generally exists no such a simple set of macro-scale field variables onto which we can project and predict the dynamics in a self-determined way. We introduce a machine-learning-based approach that enables us to systematically pass the micro-scale physical laws onto the macro-scale. The non-Newtonian hydrodynamics of polymeric fluids is used as an example to illustrate the essential idea. 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, with a new form of the objective tensor derivative, can be derived from the micro-scale model. Unlike our conventional wisdom about ML modeling, the training only uses time-discrete samples. The final model, named the deep non-Newtonian model (DeePN2), retains a multi-scaled nature with clear physical interpretation and strictly preserves the frame-indifference constraints. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.

Speaker: Professor Huan LEI
Date: 23 August 2024 (Friday)
Time: 2:00pm – 3:00pm
Poster: Click here