Machine Learning for Reparameterization of Multi-scale Closures

Scientific machine learning (ML) is becoming increasingly useful in learning closure models for multi-scale physics problems; however, many ML approaches require a vast array of training data and can struggle with generalization and interpretability. Here, rather than learning an entire closure operator, we adopt an existing reduced-dimension model of the microphysics and learn an optimal re-parameterization of the solver. We demonstrate two approaches for the training the reduced dimension closure model 1) an a priori method that optimizes the closure parameterization and the neural network parameters separately and 2) an a posteriori method that simultaneously optimizes both. We find that while each method is capable of achieving a target loss, the a posteriori method is capable of achieving the target loss with a smaller network, smaller training data sizes.