Inference of Constitutive Relation of Phase-Separated Polymers by Integrating Physics-Informed Neural Networks and Symbolic Regression

Harnessing data to discover the underlying constitutive relation of phase-separated polymers can significantly advance the fabrication of high-performance materials. This work introduces a novel data-driven method to learn the constitutive equation of diffusional transport of polymers from spatiotemporal density field. In particular, the data-driven method seamlessly integrated physics-informed neural networks for inference of approximate solution of diffusivity, and symbolic regression that form explicit expressions of diffusivity. The efficacy and robustness of this method are demonstrated by learning the distinct forms of diffusivity for the phase separation of homopolymer blends with various compositions. In addition, the data-driven method is generalized to extract the constitutive relation of homogenous chemical potential in the phase separation of homopolymer blends. The data-driven framework shows the potential for model discovery of nonlinear dynamic system from the spatiotemporal state variables.