Conservation laws in a neural network architecture: enforcing the atom balance of a Julia-based photochemical model (v0.2.0)

Abstract. Models of atmospheric phenomena provide insight into climate, air quality, and meteorology and provide a mechanism for understanding the effect of future emissions scenarios. To accurately represent atmospheric phenomena, these models consume vast quantities of computational resources. Machine learning (ML) techniques such as neural networks have the potential to emulate computationally intensive components of these models to reduce their computational burden. However, such ML surrogate models may lead to nonphysical predictions that are difficult to uncover. Here we present a neural network architecture that enforces conservation laws to numerical precision. Instead of simply predicting properties of interest, a physically interpretable hidden layer within the network predicts fluxes between properties which are subsequently related to the properties of interest. This approach is readily generalizable to physical processes where flux continuity is an essential governing equation. As an example application, we demonstrate our approach on a neural network surrogate model of photochemistry, trained to emulate a reference model that simulates formation and reaction of ozone. We design a physics-constrained neural network surrogate model of photochemistry using this approach and find that it conserves atoms as they flow between molecules while outperforming two other neural network architectures in terms of accuracy, physical consistency, and non-negativity of concentrations.