KPPax: preprocess differentiable kinetic ODE for machine learning in atmospheric chemistry

Constraining reaction rate coefficients is a central challenge in the development of explicit atmospheric chemical mechanisms, particularly for autoxidation systems where many reaction pathways are only indirectly observed through high-resolution mass spectrometry. In this study, we evaluate rate-coefficient optimisation methods for a toy-case autoxidation mechanism using synthetic data with known ground truth. Two complementary approaches are compared: ODE-constrained neural-network optimisation, which provides efficient point estimates of uncertain rate coefficients, and the Markov Chain Monte Carlo (MCMC) approach, which samples the posterior distribution of rate coefficients and quantifies parameter uncertainty. The methods are tested using direct concentration observations and mass-spectral observations under different noise levels. For unperturbed and low-noise synthetic observations, both methods converged towards the known rate coefficients, with the neural-network optimiser providing faster point estimates. Under high-noise conditions (with the signal-to-noise ratio approximately S / N = 1), however, MCMC was substantially more robust in recovering the rate coefficients. The posterior analysis shows that mass-spectral aggregation broadens credible intervals even at low noise, and that high-noise mass spectra can leave many individual reaction rates weakly identifiable. Posterior predictive validation nevertheless shows how broad parameter uncertainty constrained by MCMC remains consistent with accurate reproduction of the observable mass spectrum. These results demonstrate that point-estimation and Bayesian sampling methods provide complementary information: neural-network optimisation is effective for informative data, whereas MCMC is essential for diagnosing uncertainty, non-uniqueness, and identifiability in noisy or aggregated inverse problems.

Earth-system models simplify atmospheric chemistry into condensed mechanisms, because near-explicit mechanisms such as the Master Chemical Mechanism (MCM) are too costly to solve in every grid cell. Neural emulators could lift this limit, but most advance the chemistry in small time steps and cover only a few species or a reduced mechanism. Here we introduce FNO-MoE, a Fourier neural operator with a mixture of experts that predicts the full near-explicit chemical state over 30 minutes in a single call. The same network also guides its own training, using the disagreement among its experts to select the most informative box-model simulations. At equal cost, this active sampling yields a more accurate emulator than random or evenly spread sampling. Fine-tuning on longer trajectories keeps it stable over multi-hour runs in which models trained on short simulations diverge. The resulting emulator reproduces the evolution of thousands of species with high fidelity, remains accurate for unseen chemical compositions and runs orders of magnitude faster than the numerical solver. These results open a new direction for emulating complex atmospheric systems: neural operators that predict the full chemical state over long windows and choose their own training data. Training under changing meteorology is the next step towards bringing near-explicit chemistry into Earth-system models.

Machine learning has shown promise for physics applications, but integrating Python-based libraries into high-performance C++ solvers can create performance bottlenecks. We present CodeJeNN, which addresses this gap by auto-generating self-contained C++ code from trained Keras models for inference. This eliminates external dependencies through inlined functions, allowing seamless integration into existing frameworks. We describe the Keras-to-C++ workflow, supported architectures, and limitations. CodeJeNN is demonstrated through inference benchmarks against Keras (eager and optimized) and a computational fluid dynamics (CFD) simulation of a hydrogen-air mixing layer in which viscosity is modeled using a neural network, showing that the generated models integrate directly into a solver while remaining efficient and accurate.