Abstract

The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple lengths and time scales: electronic, atomistic, defects, domains etc. Multiscale modeling seeks to understand these interactions by exploiting the inherent hierarchy where the behavior at a coarser scale regulates and averages the behavior at a finer scale. This requires the repeated solution of computationally expensive finer-scale models, and often a priori knowledge of those aspects of the finer-scale behavior that affect the coarser scale (order parameters, state variables, descriptors, etc.). This talk reviews a number of machine learning frameworks that can be used to address the challenges in multi-scale modeling. First, we demonstrate the use of Fourier neural operators (FNOs) to accelerate the solution of governing partial differential equations of fine-scale models. We then demonstrate the use of recurrent neural operators (RNOs) to bridge the scales that is capable of providing insights into the history dependence and the macroscopic internal variables that govern the overall response. We end the talk with a discussion on how one can quantify the propagation of uncertainties through the length scales.

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