Thermo-Algorithmic Determinism in Hyperscale AI Architectures: The mCDU Data Physics Framework

Abstract

This monograph formalizes the principle of Thermo-Algorithmic Determinism in high-performance computing (HPC) and hyperscale artificial intelligence accelerator clusters. Classical systems engineering assumes a strict separation between mechanical/hydraulic infrastructure (MEP) and the logical algorithmic runtime. We demonstrate that in massive, multi-node training environments reliant on synchronous communication barriers (e.g., NCCL Ring-AllReduce), this decoupling constitutes a fundamental methodological error. We model the direct propagation of macro-scale hydraulic anomalies within the Cooling Distribution Unit (CDU)—such as cavitation, pressure pulsations, and gas desorption via Henry's Law—down to the 100–200 µm silicon microchannels of the cold plates. The resulting two-phase flow maldistribution and bubble pinning cause critical micro-scale convective degradation, leading to millisecond thermal resistance spikes and localized silicon temperature surges. To resolve the dynamic, non-linear feedback loop between leakage currents and Dynamic Voltage and Frequency Scaling (DVFS), we introduce the Mathematical Model of Thermo-Algorithmic Equivalence. By mapping physical time evolution as a function of the cumulative executed clock cycles, we derive the Cycle-Domain Phenomenological Execution Time Integral. This analytical framework accurately predicts execution times ($t_{exec}$) and cluster instability (Straggler Effects, HBM multi-bit Silent Data Corruption, and checkpoint rollbacks) driven purely by fluid dynamics, establishing hydraulic optimization as a primary unit test for AI runtimes.