LiteCast: Adaptive Carbon-Aware Forecasting

• LiteCast is a lightweight forecasting method that uses a SARIMAX model to prioritize the ranking of low- and high-carbon periods for effective carbon-aware scheduling.
• It requires only seven days of historical data and limited exogenous inputs, ensuring rapid retraining and low computational overhead for real-world applications.
• By emphasizing ranking concordance rather than traditional error metrics, LiteCast achieves up to 97% of oracle carbon savings, significantly reducing realized emissions.

LiteCast is a lightweight, adaptive time series forecasting method developed for carbon-aware optimization of electricity consumption scheduling. Grounded in the observation that realized emissions savings are primarily determined by correctly ranking low- and high-carbon periods—rather than by minimizing absolute forecast errors—LiteCast shifts the focus of carbon-intensity forecasting from pointwise metrics such as MAPE or RMSE to ranking concordance. Requiring only a minimal window of recent historical data and limited exogenous inputs, LiteCast is designed for efficient deployment in real-world scheduling systems that shift or allocate workloads in response to electricity grid carbon intensity.

1. Motivation and Theoretical Foundation

Growing variance in grid operation, driven by renewable integration and demand-response policies, has complicated carbon-aware scheduling for consumers such as data centers and electric vehicles. Conventional state-of-the-art forecasting models (e.g., CarbonCast, EnsembleCI) are optimized for low forecast error across long historical intervals, training large neural models with heavy computational and data overhead. However, empirical results show that:

• High forecast accuracy (e.g., $5\%$ MAPE) with poor ranking can lead to substantial excess emissions (up to $20\%$ more).
• In contrast, a forecast with $32\%$ MAPE but $95\%$ correct ordering can select the same low-carbon slots as an oracle scheduler.

Formally, for a job of duration $L$ within a scheduling window of $S$ slack hours, the chosen start slot is:

$$s_{\rm pred} = \arg\min_{h \in \{0, \dots, S\}} \sum_{k=0}^{L-1} \hat f_{h+k}$$

$$E_{\rm pred} = \sum_{k=0}^{L-1} f^{\rm act}_{s_{\rm pred}+k}$$

$\rho = \frac{E_{\rm pred}}{E_{\rm oracle}}$

where $E_{\rm oracle}$ denotes minimum possible (oracle) emissions. LiteCast is architected to drive $\rho \rightarrow 1$ by prioritizing preservation of the forecasted time-ordering of carbon intensity values.

2. Data Requirements and Input Features

LiteCast operates solely with publicly available, hourly aggregated inputs:

• Regional generation mix (coal, gas, oil, nuclear, hydro, wind, solar, batteries), sourced from EIA (US) and ENTSO-E (EU).
• Lifecycle/direct carbon-emission factors for each generation type, from IPCC guidelines.
• Weather forecasts (temperature, humidity, wind speed, solar irradiance) from NSF/NCAR RDA.
• Electricity demand forecasts from grid operators or standard time-series tools.

Notably, LiteCast requires only seven days of recent history to capture relevant autocorrelations, diurnal and weekly seasonality, and to issue multi-day forecasts. This minimal requirement sharply contrasts with deep learning models utilizing years of history, enabling both rapid retraining and easy integration into operational pipelines.

3. Model Architecture and Forecast Mechanism

At its core, LiteCast employs a SARIMAX model (Seasonal ARIMA with exogenous regressors) for each source fraction $y_t$:

$$\begin{aligned} y_t =\;& \phi_1 y_{t-1} + \Phi_1 y_{t-24} + \theta_1\epsilon_{t-1} + \Theta_1\epsilon_{t-24} \ & - \Phi_1y_{t-25} + \Theta_1\epsilon_{t-25} + {\boldsymbol\beta}^\top \mathbf{x}_t + \epsilon_t \end{aligned}$$

where

• $\phi_1, \Phi_1$: AR terms (lag-1, daily seasonality),
• $\theta_1, \Theta_1$: MA terms (lag-1, daily seasonality),
• $\boldsymbol\beta$: weights for exogenous features $\mathbf{x}_t$ (weather, demand, hour-of-day/week),
• $\epsilon_t$: white noise innovation.

After forecasting the fraction of each generation source, the model reconstructs hourly carbon intensity as:

$$\hat f_t = \sum_{i \in \{\text{coal, gas, ...}\}} \left( \widehat{\text{share}_{i,t}} \right) \times (\mathrm{gCO}_2/\mathrm{kWh})_i$$

This architecture deliberately avoids black-box deep models, ensuring interpretability and low resource consumption while still capturing both autocorrelation structures and exogenous influence.

4. Concordance-Driven Objective and Evaluation

Rather than optimizing traditional errors (MAPE, RMSE), LiteCast maximizes the pairwise concordance between predicted and actual ranking of time slots, formalized via the concordance index (CI):

$$\mathrm{CI}(\hat f, f^\star) = \frac{1}{\binom{n}{2}} \sum_{0 \leq i < j < n} \mathbf{1}\left[ (\hat f_i < \hat f_j) = (f^\star_i < f^\star_j) \right]$$

where $f^\star$ is the ground-truth carbon intensity. A CI of $1$ indicates perfect ordering. Empirical results demonstrate that a $+15\%$ gain in CI translates to a two-fold reduction in realized emissions, while analogous improvements in MAPE yield negligible gains. Thus, LiteCast's design aligns directly with the scheduling objective: preserve low-carbon window orderings.

5. Adaptivity and Dynamic Scheduling

LiteCast is designed for rapid adaptivity to grid changes. Leveraging the SARIMAX model and short historical horizon, LiteCast retrains in seconds as new observations arrive. A dynamic scheduling heuristic iteratively refines job allocations in response to updated forecasts:

UpdateSchedule()

1. At each time $t$, for unscheduled jobs, merge new energy/weather data.
2. Retrain LiteCast on the latest seven days.
3. If the new CI surpasses the original and emissions are reduced, recompute start time or interruptible slots.

This retraining loop enables near-real-time response to renewable fluctuations, generator contingencies, or demand spikes. LiteCast thus facilitates opportunistic exploitation of low-carbon intervals with minimal computational latency.

6. Computational Efficiency and Scalability

In contrast to deep-learning baselines that require months of training data and significant compute (e.g., GPU clusters), LiteCast has the following resource profile:

Method	Historical Data Amount	Training Time	Hardware
LiteCast	7 days	Seconds (per region)	Single CPU core, minimal
SOTA Deep	Years	Hours (per region)	Multi-GPU or clusters

LiteCast’s deterministic, low-memory design is well suited for on-premises deployment in private clouds, edge sites, or grid operator toolchains.

7. Empirical Performance and Applications

LiteCast was evaluated across 50 balancing regions (U.S., Europe; 2023 data) in multiple operational scenarios:

• Temporal Scheduling: Flexible jobs (1–48 hours, slack up to 168 hours), both continuous and checkpointable-intensive.
• Spatial Scheduling: Assigning jobs across grids to minimize emissions.
• HPC Replay: Scheduling the ForHLR II KIT supercomputer’s mixed batch workload.

Key reported outcomes:

• LiteCast outperformed CarbonCast with $20\%$ higher realized carbon savings.
• The dynamic heuristic achieved $97\%$ of oracle-optimum savings ($\rho = 0.97$), compared to $\rho \approx 0.8$ for CarbonCast.
• In highly variable renewable regions (e.g., Denmark, ERCOT), additional emissions remained $<10\%$ for 24h slacks; benchmarks were up to $25\%$.
• KIT cluster replay: LiteCast reduced emissions by $3.4\%$ (oracle: $5.4\%$), surpassing CarbonCast in $93\%$ of regions.

A plausible implication is that further improvements to raw pointwise forecast accuracy do not yield proportional practical benefit for carbon-aware optimization. Instead, efficiency, interpretability, and adaptive retraining aligned to scheduling objectives are more critical.

Conclusion

LiteCast exemplifies the effectiveness of lightweight, ranking-oriented forecasting for carbon-optimized scheduling. By prioritizing concordance, leveraging only seven days of history, and allowing rapid retraining, LiteCast achieves $97\%$ of possible carbon savings at a small fraction of the data and compute cost required by black-box models. This suggests that future work in carbon-aware optimization would benefit from focusing on ranking preservation and efficient adaptation rather than on further incremental reductions in standard forecast error metrics.