Physics-informed data-driven closure relation for dilute short fiber suspensions

Abstract Tensor based formulations for modeling fiber orientation require the use of a closure approximation to solve the macro-descriptor evolution equation. This originates from the hydrodynamic component of motion and has received some attention in literature. In this work, we use the concept of universal ordinary differential equations to infer a data-driven closure for fibers in the diluted regime using simple homogeneous flows. The closure can be understood as an orthogonal correction to the linear closure in eigenspace. To simplify and accelerate the training process, empirically determined bounds are used to restrain the machine learning output to physically admissible values. Three sets of tests are used to assess the performance of the model with simple homogeneous flows not included in the training pool, sequential combination of simple flows, and a non-homogeneous flow in a center gated disk. The results show that the trained model is able to adequately replicate the true dynamics of orientation, even for unseen flow regimes.