Prognostic tracer advection in Numerical Weather Prediction scales linearly with increasing number of species, resulting in major bottleneck in Numerical Weather Prediction simulation involving high number of tracer species, e.g. Atmospheric Chemistry simulation where 10s-100s tracers must be advected independently at each advection time step. This thesis investigates whether a physically consistent reduced order representation can serve as a computationally beneficial surrogate for the tracer transport operator in the ICON-ART model. By using mineral dust experiment–a standard test suite in ICON-ART–as a pilot study, 4 embedding models with increasing level of complexity are developed and evaluated in an offline training & evaluation framework: baseline Principle Component Analysis (PCA), Non-negative Matrix Factorisation (NMF), a Gradient based PCA (1 layer Autoencoder with no activation function), and a novel Multi-head Autoencoder that decouples magnitude construction from zero/non-zero classification through a split Softplus and Sigmoid decoder heads, broadly expanding the dynamic range of the output and ensuring non-zero, well defined gradient across the entire interval of output. ... mehrPCA achieves the lowest reconstruction error (total normalised RMSE ∼ 1% at 4 latent dimensions) with exact idempotency under iteration. However, the mean centred property, unconstrained basis vector rotation and the absence of non-negativity constraint, making it unsuitable for operational deployment, only serving as a theoretical lower bound of degrees of freedom of the manifold. NMF preserves non-negativity by construction, underestimates concentration with high absolute magnitude while overestimates the counterpart, denoting a "drift to centre" property. It suffers from a zero-variable problem, whereby near-zero/zero concentrations exhibited strong variance (ghost mass) for species with high absolute concentration, warranting the need for a zero/non-zero classifier head. Gradient PCA fails completely in lower absolute concentration, where mass concentration dust A, O(1 − 6) smaller than other species, exhibiting strong variance (up to 70x to the species magnitude), further intensify the need for a classifier head. Conventional Autoencoder examined in the ablation study, collapses to a narrow output band. Close examination of the gradient of the Autoencoder revealed that this behaviour is structurally determined, as vanishing gradient problem occurs at |ℎ| ≈ 8.67 in float32 precision. The proposed Multi-head Autoencoder addresses the limitations by employing an additional non-zero head (Sigmoid, interval (0, 1)), in addition to the magnitude head (Softplus, interval (0, ∞)) , whose element-wise product extends the effective output dynamic range. Gradient analysis demonstrates that the 3 backpropagation pathways operation in complementary regime: the BCE classifier dominates at zero elements, preserving classification accuracy, while the magnitude head (MSE Loss) dominates at non-zero elements, preserving concentration fidelity. The model achieves strong single-pass reconstruction for Dust B-Ci (higher absolute magnitude pair, 𝑅2 = 0.82 − 0.91, 𝑛𝑅𝑀𝑆𝐸 ∼ 10 − 14%), and optimal manifold preservation (total ACC=0.9986, normalised Wasserstein with IQR = 0.0035). However, the iterative stability limits its practicality at the current state: total mass degrades to 80.7% after 100 offline iterations, possibly driven by the asymptotic Sigmoid gate (𝜎 < 1 by construction) and unbounded error growth. Error in the FULL MODEL testing dataset sharply collocates with connectively active regions under spatial analysis. This is attributed to the training strategy, where a no-source-sink (convective and other source and sink terms are turned off) dataset are used for dataset training, which excludes the corresponding sub-manifold geometry from the training data, limiting the generalisability to these domains. A proxy timing study with PyTorch-ComIn-ICON coupling revealed a 21% reduction in advection cost, fall within the expected range, suggesting that the approach is computationally attractive, even after I/O bottleneck in host-machine learning model coupling is considered. The author therefore concludes that, a reduced order tracer embedding for ICON-ART is indeed feasible in principle, however, no model simultaneously satisfies all physical criterion set in the beginning of the assize–non-negativity, mass conservation, manifold preservation and iterative stability–at level sufficient for operational deployment. Architectural improvements, including a steepened Sigmoid gate, auxiliary mass-conservation head and GPU/native Fortran coupling are proposed as directions for future work.
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