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The Accuracy-Efficiency Paradox Quantifying Net Energy Loss in on-Device Energy Forecasting
Jaeik Jeong, Tai-Yeon Ku, Wan-Ki Park
TL;DR
Energy forecasting commonly treats higher accuracy as inherently more energy-efficient, but complex on-device models also consume inference energy and can accelerate battery aging. The paper proposes a TCO framework that unifies forecasting error, inference energy, and degradation, finding that thermal conditions can reverse which model is most efficient. Its evaluation is limited to simple hour-ahead residential tasks and a small set of baseline models.
Problem
On-device forecasting frameworks often prioritize predictive precision while evaluating forecasting performance separately from inference energy and battery aging.
Method
The paper proposes a TCO framework that treats forecasting error, inference energy consumption, and battery aging as a unified energy-loss metric.
Results
The Transformer has the lowest TCO when k < 0.08 but becomes least efficient when k > 0.22; at k = 20, LR eventually outperforms MLP and Transformer.
Takeaways & Limitations
The optimal forecasting model depends on operating conditions because thermal degradation costs can outweigh superior predictive performance.
Takeaways & Limitations
The evaluation is limited to simple hour-ahead residential forecasting tasks and a small set of baseline models.
Abstract
from arXiv · showhide
Energy forecasting aims to maximize accuracy to ensure energy efficiency by reducing energy waste, an objective that applies equally to on-device forecasting for mission-critical edge environments, including military systems. However, this paper identifies the Accuracy-Efficiency Paradox: high-precision energy forecasting models can ironically trigger a net energy deficit. This stems from both edge AI's inference energy consumption and battery aging. We propose a Total Cost of Ownership (TCO) framework for energy forecasting, designed to minimize net energy loss. This framework treats not only inference energy consumption but also battery aging as a unified form of energy loss, as degradation represents a physical dissipation of the system's future energy-carrying capacity. We demonstrate that in thermally sensitive edge environments, energy saved by the superior precision of complex architectures is often outweighed by the total energy lost through their high operational intensity.
I. INTRODUCTION
On-device energy forecasting creates an Accuracy-Efficiency Paradox: complex models may reduce forecasting error while increasing inference energy use and thermally accelerated battery aging. The paper addresses this gap by unifying these costs with forecasting error in a TCO objective.
- Accuracy-Efficiency Paradox: High-complexity models can offset marginal forecasting-error savings through inference energy consumption and exponentially accelerated battery aging.Localized thermal stress links operational intensity to faster battery degradation.
- Research gap: Most existing frameworks evaluate forecasting performance separately from the operational costs of inference and battery aging.Prior work on these energy costs has also largely treated them in isolation.
- Proposed solution: The proposed TCO objective unifies forecasting error, inference energy consumption, and battery aging as a single energy-loss metric.Battery aging is treated as irreversible loss of embodied energy and future energy-carrying potential.
- Proposed solution: The framework mathematically identifies thresholds where improved forecasting accuracy produces net system energy loss.This directly targets the paradox between predictive precision and total energy cost.
II. METHODOLOGY
The methodology evaluates on-device forecasting through a unified TCO metric that includes forecasting accuracy, inference energy, and battery aging.
- Unified evaluation framework: The evaluation framework integrates Arrhenius-derived battery aging cost into TCO to quantify net energy efficiency.TCO combines battery degradation with on-device forecasting costs rather than treating accuracy alone as the objective.
A. Derivation of Battery Aging Cost
The derivation connects inference energy to heat generation, temperature rise, Arrhenius acceleration of aging, and additional battery-aging cost. In thermally sensitive environments, higher inference energy therefore produces an exponentially increasing aging penalty.
- Arrhenius aging model: The acceleration factor AF is derived from the Arrhenius equation using activation energy, Boltzmann’s constant, nominal temperature, and stress temperature.ΔT = Tstress−Tuse represents the localized temperature rise induced by computation.
- Heat generation: Inference energy Z is modeled as dissipated internal heat Q in compact, fanless edge devices.The framework uses Q ≈ 3600·Z to convert watt-hours into joules before calculating temperature rise.
- Arrhenius aging model: Treating temperature-related terms as environmental constant k simplifies the model to AF = exp(k · 3600 · Z).This expresses exponentially increasing aging acceleration as inference energy rises.
- Battery-aging cost: Additional aging equals (AF−1)·r·Δtstress, where r is the baseline aging rate and Δtstress is elevated thermal-stress duration.The resulting quantity is converted into the additional aging cost Caging.
B. Total Cost of Ownership (TCO) Formulation
The TCO formulation unifies forecasting error, inference energy, and battery aging as a single energy-loss metric for selecting efficient on-device forecasting models.
- TCO Formulation: TCO_t combines forecasting error, inference energy consumption, and battery aging into one energy-inefficiency metric.Forecasting error represents system-level waste, inference energy represents direct intelligence-related waste, and battery degradation represents lost future energy-carrying capacity.
- TCO Formulation: The framework assigns coefficients to forecasting-error penalty, operational cost, and hardware lifetime cost.The coefficients are denoted c_p, c_o, and c_l, respectively.
- TCO Optimization: The optimization engine minimizes cumulative energy footprint rather than forecasting error alone.It integrates real-time inference-energy monitoring with Arrhenius-derived battery aging to identify cases where a nominally superior model becomes inferior because of physical overhead.
III. EXPERIMENT
The experiment numerically evaluates the TCO framework on real-world data to examine how environmental factors and operational intensity affect model selection.
- Evaluation Framework: The evaluation uses numerical experiments with real-world data to assess the TCO framework.
- Evaluation Framework: The study examines how environmental factors and operational intensity shift the optimal forecasting model choice.
- Evaluation Framework: The evaluation is designed to demonstrate the accuracy-efficiency trade-off in on-device energy forecasting.
A. Dataset and Preprocessing
The study uses a high-resolution residential energy dataset from Yeosu-si with hourly measurements and chronological train-validation-test partitioning.
- Dataset: The dataset contains 8,760 hourly residential energy-consumption samples from Yeosu-si collected between September 2021 and August 2022.Measurements are recorded to three decimal places in kWh, enabling detection of marginal forecasting improvements.
- Preprocessing: The data are chronologically divided into ten months for training, one month for validation, and one month for testing.
- Preprocessing: All training values are normalized with min-max scaling to support stable gradient descent.
B. Predictive Models and Training Strategy
The experiment compares forecasting models with increasing complexity and trains neural models using tuned optimization, early stopping, and a 24-hour sliding window.
- Predictive Models: Linear Regression, MLP, and Transformer represent low-, intermediate-, and high-complexity forecasting models.Linear Regression is the minimal-overhead baseline, while the MLP uses two fully connected layers with 64 hidden units and ReLU activation.
- Training Strategy: The MLP and Transformer are trained with Adam using learning rates from 0.0001 to 0.001 selected by grid search.
- Training Strategy: Early stopping selects training based on minimum validation-set Mean Absolute Error.
- Forecasting Setup: Each model uses the preceding 24 hours as input for hour-ahead forecasting.
C. Experimental Results and Analysis
The experiments show that model choice depends on thermal sensitivity: accuracy gains can be outweighed by inference-driven battery aging, changing which model minimizes TCO over time.
- MLP and Transformer improve MAE over LR by 1.7% and 2.7%, respectively, while the Transformer requires disproportionally higher inference energy.The inference energy Z remains several orders of magnitude smaller than forecasting error, but its effect on battery aging is amplified exponentially.
- At k < 0.08, the Transformer achieves the lowest TCO because its accuracy advantage outweighs minimal battery aging costs.The cost coefficients cp, co, and cl are all set to 1 in this comparison.
- At k > 0.22, the Transformer becomes the least efficient choice as its TCO escalates exponentially with thermal sensitivity.Poorly cooled edge environments correspond to higher k values.
- At k > 18.0, the MLP exhibits the same TCO paradox relative to the LR baseline.
- The crossovers show that the optimal model depends on the operating environment, even when inference-energy differences are negligible.
- Over 48 hours at k = 20, LR eventually outperforms MLP and becomes optimal as Transformer TCO escalates almost immediately.In stable environments with k = 0 to 0.3, the optimal choice shifts from Transformer to MLP as battery aging costs rise.
IV. DISCUSSION
The discussion identifies scope and modeling limitations: the evaluation uses simple residential forecasting, while broader deployments change which operational and aging costs dominate.
- The analysis uses simplified assumptions about thermal behavior, battery aging dynamics, and inference-to-heat conversion.Empirically characterizing realistic k and cost coefficients under diverse conditions is identified as a next step.
- The experimental evaluation is limited to simple hour-ahead residential forecasting with a small set of baseline models.More complex multistep-ahead and multi-site tasks require examining the TCO paradox with more sophisticated ANN models.
- TCO components are context-dependent: federated learning adds local-training energy, while data centers add cooling energy and rely less on battery aging.In federated learning, local training can rival battery-aging impact; in data centers, ESS aging is less critical, especially for VRFBs.
V. CONCLUSION
The TCO framework addresses the Accuracy-Efficiency Paradox by integrating forecasting accuracy, inference energy consumption, and battery aging. Results show that high operational intensity can offset the benefits of superior accuracy in thermally constrained edge environments.
- The TCO framework integrates energy forecasting accuracy, inference energy consumption, and battery aging into a holistic evaluation perspective.
- Superior accuracy does not inherently ensure system-level efficiency when high operational intensity accelerates battery aging.
- Marginal performance gains from high-complexity models are often offset by exponential battery aging costs in thermally constrained environments.
- The framework supports deployment of energy-aware edge models by balancing computational intelligence with physical reliability.