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Energy Flow Graph: Modeling Software Energy Consumption

Saurabhsingh Rajput, Tushar Sharma

Abstract

The growing energy demands of computational systems necessitate a fundamental shift from performance-centric design to one that treats energy consumption as one of the primary design considerations. Current approaches treat energy consumption as an aggregate, deterministic property, overlooking the path-dependent nature of computation, where different execution paths through the same software consume dramatically different energy. We introduce the Energy Flow Graph (EFG), a formal model that represents computational processes as state-transition systems with energy costs for both states and transitions. EFG enables various applications in software engineering, including static analysis of energy-optimal execution paths and a multiplicative cascade model that predicts combined optimization effects without exhaustive testing. Our early experiments demonstrate EFG's versatility across domains: in software programs validated through 3.5 million executions, 15.6% of solutions exhibit high path-dependent variance (CV $>$ 0.1), while structural optimization reveals up to 705$\times$ energy reduction. In AI pipelines, the cascade model predicts optimization combinations within 5.1% error, enabling selection from 4.2 million possibilities using only 22 measurements. The EFG transforms energy optimization from trial-and-error to systematic analysis, providing a foundation for green software engineering across computational domains.

Energy Flow Graph: Modeling Software Energy Consumption

Abstract

The growing energy demands of computational systems necessitate a fundamental shift from performance-centric design to one that treats energy consumption as one of the primary design considerations. Current approaches treat energy consumption as an aggregate, deterministic property, overlooking the path-dependent nature of computation, where different execution paths through the same software consume dramatically different energy. We introduce the Energy Flow Graph (EFG), a formal model that represents computational processes as state-transition systems with energy costs for both states and transitions. EFG enables various applications in software engineering, including static analysis of energy-optimal execution paths and a multiplicative cascade model that predicts combined optimization effects without exhaustive testing. Our early experiments demonstrate EFG's versatility across domains: in software programs validated through 3.5 million executions, 15.6% of solutions exhibit high path-dependent variance (CV 0.1), while structural optimization reveals up to 705 energy reduction. In AI pipelines, the cascade model predicts optimization combinations within 5.1% error, enabling selection from 4.2 million possibilities using only 22 measurements. The EFG transforms energy optimization from trial-and-error to systematic analysis, providing a foundation for green software engineering across computational domains.
Paper Structure (15 sections, 6 equations, 1 figure, 2 tables)

This paper contains 15 sections, 6 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Energy Flow Graph (efg)
  3. Definition
  4. Energy Analysis Methods
  5. Deterministic Path Analysis (Bounds & Traces)
  6. Stochastic Path Analysis
  7. Energy Optimization Constructs
  8. Applications
  9. Case Study 1: Algorithmic Energy Analysis
  10. Case Study 2: AI Pipeline Optimization
  11. Threats to Validity
  12. Related Work
  13. Implications
  14. Future Plans
  15. Conclusions

Figures (1)

  • Figure 1: Energy variance analysis. (a) Path dependency: intra-solution CV distribution; 15.6% with $CV > 0.1$ validate stochastic modeling. (b) Structural impact: 42% of problems offer $>90\%$ energy reduction via topology selection. (c) Thermodynamic variance: power vs. runtime (log scale); $\sigma=33.6$W validates non-uniform state costs $\mathcal{C}_s$.

Theorems & Definitions (1)

  • definition 1: Energy Flow Graph