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Modeling atmospheric chemistry is computationally expensive and limits the
widespread use of atmospheric chemical transport models. This computational
cost arises from solving high-dimensional systems of stiff differential
equations. Previous work has demonstrated the promise of machine learning (ML)
to accelerate air quality model simulations but has suffered from numerical
instability during long-term simulations. This may be because previous ML-based
efforts have relied on explicit Euler time integration -- which is known to be
unstable for stiff systems -- and have used neural networks which are prone to
overfitting. We hypothesize that the creation of parsimonious models combined
with modern numerical integration techniques can overcome this limitation.
Using a small-scale photochemical mechanism to explore the potential of these
methods, we have created a machine-learned surrogate by (1) reducing
dimensionality using singular value decomposition to create an
interpretably-compressed low-dimensional latent space, and (2) using Sparse
Identification of Nonlinear Dynamics (SINDy) to create a
differential-equation-based representation of the underlying chemical dynamics
in the compressed latent space with reduced numerical stiffness. The root mean
square error of the ML model prediction for ozone concentration over nine days
is 37.8% of the root mean concentration across all simulations in our testing
dataset. The surrogate model is 11$\times$ faster with 12$\times$ fewer
integration timesteps compared to the reference model and is numerically stable
in all tested simulations. Overall, we find that SINDy can be used to create
fast, stable, and accurate surrogates of a simple photochemical mechanism. In
future work, we will explore the application of this method to more detailed
mechanisms and their use in large-scale simulations.