Multiscale Modeling of History-Dependent Materials Using Continuous-Time Neural Operators

We apply a Continuous-Time Recurrent Neural Operator (CT-RNO) framework to capture the nonlinear, history-dependent behavior of heterogeneous materials across atomistic and continuum scales. The CT-RNO formulation evolves material states continuously in time, removing numerical instabilities associated with discrete integration while preserving key physical trends. By learning microscopic dynamics and bridging scales through homogenization, the model reproduces path-dependent constitutive behavior—such as hysteresis and rate effects—with remarkable accuracy and efficiency. Demonstrations on atomistic-to-continuum systems and electrohydrodynamic flows show that CT-RNO achieves predictive fidelity comparable to full simulations while reducing computational cost by several orders of magnitude. This approach highlights the promise of continuous-time operator learning for physics-consistent, data-driven multiscale modeling of complex materials.