industrial data engineers

Abstract: Industrial systems continuously generate time series that vary in sampling frequency, scale, dynamics, and operating regime. Consequently a single time-series foundation model may not be able to represent all regimes effectively and retraining a large model for every new dataset or regime shift is computationally expensive. Modular foundation models address this issue by reusing specialised encoders trained on diverse datasets and by allowing the expansion of capabilities through the addition of new experts. This approach requires compact experts to minimize storage cost and a proper selection mechanism of experts for unseen data. We propose a modular foundation model framework that combines end-to-end Bayesian encoder training with uncertainty based routing. Using Singular Bayesian Neural Networks (SBNNs), we build a collection of compact Bayesian encoders whose epistemic uncertainty guides label-free selection. At the selected ranks, our Bayesian collection uses 63.8\% less storage than its deterministic counterpart. We evaluate this framework on time-series data through distribution shift, encoder selection, and probabilistic forecasting. Across seven incoming datasets, uncertainty-based routing is competitive with distance-based routing in terms of forecast MSE, while reducing average ECE from 0.086 to 0.072 and average NLL from 0.907 to 0.836. It also increases PICP90 from 82.28\% to 89.03\%. In a separate model-family comparison, we evaluate the SBNN pipeline against full-rank Bayes by Backprop, deep ensembles, and MC Dropout. The SBNN pipeline achieves an average MSE of 0.390, comparable with 0.396 for deep ensembles, 0.389 for MC dropout, and 0.443 for the full-rank Bayesian model. It uses 63.9\% fewer parameters than MC dropout, 81.9\% fewer than the full-rank model, and 92.8\% fewer than the deep ensemble.

Abstract: Time Series Foundation Models (TSFMs) offer strong zero-shot forecasting capabilities, but their high pretraining cost raises a practical sustainability question: does this upfront investment pay off over a full deployment lifecycle, compared to supervised standalone models that must be periodically retrained? We model the cumulative carbon cost of different approaches across a realistic industrial scenario: Chronos-2 amortizes its pretraining cost within months for large or frequently queried deployments, but a classical model remains cheaper indefinitely for small or rarely queried ones. For cases where reducing the TSFM's own cost matters, we show that removing a single encoder block (7.9% of parameters) via a gradient-free pruning criterion yields a consistent 6 to 9% reduction in FLOPs, CO2 emissions, and latency, at essentially no cost to zero-shot forecasting performance across a 25-task benchmark.

Abstract: Federated clustering methods that do not require the global number of clusters $K$ still assume that each client knows its local number $K_g$. This assumption is hard to justify when clients know no more about their data than the server does, as in fault diagnosis across independently operated industrial sites. We propose a two-phase framework in which neither count is known: each client first estimates $K_g$ from its own data, and an aggregator that requires local counts, such as FedGEM, then uses these estimates in place of the true values. For the first phase we introduce Adaptive Split--Merge (ASM), which grows a spherical Gaussian mixture by BIC-driven splitting and then merges excess components. ASM uses no labels, selects its hyperparameters on held-out client data only, and makes no assumption about how clusters are shared across clients. We derive a closed-form split criterion whose critical cluster size falls with anisotropy and rises with dimension, and show empirically that over-fragmentation grows with the number of points per cluster, which federation divides among clients. Across eight datasets, ASM with FedGEM attains a mean ARI of 0.333, against 0.256 for the next best label-free estimator and 0.361 when the true local counts are supplied. It also gives the most reliable global estimates of $K$ and is robust when client size is decoupled from local cardinality.