Foundations for FMU Surrogate Model Design in ExaDigiT: Preliminary Analysis of Three IBM POWER9 Cooling Systems

High-fidelity Functional Mock-up Unit (FMU) simulations of data-center cooling systems are accurate but computationally expensive for real-time control and rapid scenario exploration that sustainable, large-scale, high-performance computing (HPC) systems demand. Replacing these simulators with efficient deep learning surrogates is a key step toward energy-aware digital twins. But effective surrogate design requires a prior understanding of the input-output relationships, temporal dynamics, non-linearities, and spatial coupling. This work addresses that gap through a systematic statistical analysis of FMU simulation data from three IBM POWER9 cooling systems: Marconi100, Summit, and Lassen, all within the ExaDigiT framework. Key findings are (i) a structural decoupling between the primary and secondary loops, as the primary loop is actively managed and substantially non-linear and load-following, whereas the secondary loop is passive with outputs remaining practically constant regardless of inputs; (ii) level-driven dynamics (median rate/level ratio = 0.33) with 54% of pathways exhibiting higherorder transient responses and Autocorrelation Function (ACF) persistence beyond 1,000 lags, mandating recurrent or attention-based temporal architectures; (iii) negligible inter-CDU (Cooling Distribution Unit) thermal propagation that was confirmed by distance-independent correlations and asymmetry ratio Rasym = 0.95. Which allows scalable per-CDU modeling; and (iv) near-zero thermodynamic violations with tolerance-calibrated energy conservation constraints. These results yield concrete surrogate design principles for surrogate architecture selection, feature engineering, and physics-regularized training.