Green Computing and Artificial Intelligence Infrastructure: Design, Mathematical Modeling, and Experimental Evaluation of the AI Environmental Impact Framework (AI-EIF)

Abstract

The rapid expansion of artificial intelligence (AI) systems has introduced substantial yet largely unquantifiable environmental costs. Existing green computing standards such as Power Usage Effectiveness (PUE), Carbon Usage Effectiveness (CUE), and Software Carbon Intensity (SCI) were developed for legacy data centers and fail to capture the multi-faceted ecological footprint of modern AI workloads. To address this limitation, this paper introduces the AI Environmental Impact Framework (AI-EIF), a novel four-pillar framework combining energy consumption, carbon emissions, resource depletion, and standardized measurement metrics. Mathematically formalized through 10 core equations, AI-EIF is operationalized via the AI-EIF-Eval algorithm with an efficient computational complexity of O (k * p). Experimental validation conducted on the Google Cluster Trace v3 dataset spanning 3,847 AI-class workloads across eight cluster configurations demonstrates that AI-EIF-Eval achieves 94.3% measurement accuracy, surpassing SCI, CarbonTracker, and MLPerf-Energy by 15.7, 13.1, and 10.6 percentage points, respectively. Application of the framework yielded mean reductions of 38.4% in energy consumption, 41.2% in carbon emissions, and 22.7% in water usage, while driving a 47.3% increase in the composite GreenFLOPS Index. AI-EIF is unique in introducing cross-dimensional linkage (CDL) modelling, part of the 9-metric Green AI Metrics Suite (GAMS), and introducing a composite GreenFLOPS scoring index as the first unified environmental benchmarking tool for AI infrastructure. Comparative analysis to ten frameworks existing in the literature shows that AI-EIF has a dimensional coverage of 5.0/5.0, while all the rest have a maximum of 3.0/5.0. These contributions provide a robust basis for sustainable AI policy, benchmarking and regulation.