Operator Replacement Using Machine Learning with Conservation Laws

Abstract:

Machine learning tools like neural networks can be used to emulate physical systems. For this reason, ML emulators have potential to serve as operator replacements of the more computationally intensive processes in air quality and climate models, which include aerosol dynamics, gas chemistry, and radiative transfer. However, training an emulator to simply predict quantities like concentration or energy density might not guarantee physically consistent results. We develop a framework that can conserve key properties, like mass for aerosol/gas chemistry operators and energy for radiative transfer operators, to machine precision. This approach includes relating fluxes to their quantities in a linear system that guarantees balance, and derivation of a flux adjustment scheme to ensure that all concentrations remain non-negative.