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

Abstract

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 compute-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. 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. As an example, 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 to machine precision, while outperforming a naïve neural network in terms of accuracy and non-negativity of concentrations.

Physics informed deep neural network embedded in a chemical transport model for the Amazon rainforest

“…Predicting fluxes instead of absolute concentrations ensures the preservation of mass balance between gas-and particle phases of IEPOX-SOA and prevents the model from deviating far from the outputs over longer time periods. Consistently, Strum et al 18 showed that by training the emulator to predict the flux information, nonphysical predictions by the emulators can be avoided.…”

“…Also, our training data are highly nonlinear and represent complex physics and chemistry. DNNs are artificial neural networks and are widely 2 Outputs (nmol/m 3 s −1 ) particle Iepox organosulfate Flux [Bin:1-20] iepoxosFluxes particle Tetrol Flux [Bin: [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] tetrolFluxes…”

“…The work of ref. 18 showed that emulating fluxes rather than absolute concentrations obeys mass conservation much better than emulating the concentrations. A schematic of the emulator architecture used in this study for the WRF-Chem DNN-embedded model is shown in Supplementary Fig.…”

“…For our current work, we ensure that the predictions of the DNN model are bounded by using the flux data-based training approach presented in ref. 18 . Our results show that the embedded WRF-DNN model accurately simulates IEPOX-SOA components (2methyltetrols and organosulfates) within each of the 20 size bins, and maintains mass balance between gas and particle phases.…”

“…Input and output variables used for training the 20 DNNs corresponding to each of the 20 particulate size bins. + ion concentration (mol/kg-water) PHW_BIN [Bin:1-20] Total particle radius (cm) RTOTAL [Bin:1-20]Radius of the aqueous core (cm) RAQ [Bin:[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] …”