An ounce of prevention is worth a pound of cure.

Benjamin Franklin

1. of Humidity Forecasting for Reliable Data Centers

As the power requirements of AI skyrocket, the infrastructure that makes it all possible is pushing against limited resources. By 2028, new research shows that AI could consume electricity that is equal to 22% of all US households [1]. Racks of high-performance AI chips consume at least 10 times as much power as conventional servers in data centers. Accordingly, an enormous amount of heat is produced, and cooling systems take up most of the building space [2]. In addition to its carbon footprint, AI also has a substantial water footprint, much of it in regions of already high-water stress. For example, GPT-3 requires 5.4 million liters of water to train in Microsoft’s US data centers [3]. Seasonal forecasting is critical to the daily operation of equipment inside data centers. Weather conditions, such as temperature and humidity, affect how intensely cooling systems inside data centers must work [4].

In this article, the forecast of humidity is computed in several ways. A better forecast of temperature and humidity can enable more efficient load planning, optimization of cooling schedules, and less demand placed on power and local water sources. Now, since we’re primarily discussing humidity in this article, let us see what the effects of its extreme values are:

• High humidity: Condensation becomes a big issue — it can corrode hardware and trigger electrical failures. It also makes chillers work harder, costing more energy and water.
• Low humidity: The danger flips: static and ESD (electrostatic discharge) can build up and fry sensitive chips.

Accurate forecasting of humidity can help:

• Fine-tune cooling schedules
• Determine demand peaks
• Schedule maintenance
• Redistribute workloads before environmental conditions cause costly downtime

By implementing the above protective measures, we reduce the strain on electricity and local water supplies, ensuring the resilience of AI centers and the overall efficiency of the distributed computing infrastructure.

It is not only data centers that can be affected by humidity; edge devices, such as sensors, can be affected as well. These are more vulnerable to weather conditions because they are typically outdoors and in remote areas. Edge applications often need low-latency predictions. This favors lighter algorithms, such as XGBoost. For this reason, in the forecasting section below, XGBoost and other light algorithms are discussed.

Let us conclude this section by discussing the futuristic cover image of a data center located on the Moon. Lunar data centers would be impervious to many of Earth’s constraints, such as extreme weather and earthquakes. In addition, the Moon offers a perfectly neutral place for data ownership. As a matter of fact, on 26th February 2025, SpaceX launched a Falcon 9 rocket that carried Intuitive Machines Athena lunar lander [5]. Among other things, Athena contained a small data center, called Freedom, developed by Lonestar Holdings. Athena could not manage a full upright landing, however, Freedom performed successful data operations prior to landing. In addition, despite the fact that the Athena lander landed inside a crater, the Freedom data center survived and demonstrated the possibility of a lunar data center [6].

2. A Real-World Case Study: Forecasting Humidity With a Precision Interval

Given the importance of weather forecasting for data centers, I turned to a real-world dataset from Kaggle containing daily climate measurements from Delhi. India has a robust data center industry. According to DataCenters.com [7], Delhi currently has 30 data centers, and a Delhi developer will invest $2 billion to further expand the India data center growth [8].

The data contain temperature, humidity, wind speed, and atmospheric pressure measurements. A training set is provided on which we trained our models, and a test set, on which we tested the models. The link to the *Kaggle *data and information about its license can be found in the footnote of this article.

Although temperature, wind, and pressure all influence cooling demand, I focused on humidity because it plays an important role in evaporative cooling and water consumption. Humidity also changes more rapidly than temperature, and therefore, it is a very meaningful target for predictive modeling.

I began with classical approaches such as AutoARIMA, then moved to more flexible models like Facebook’s Prophet and XGBoost, and concluded with deep learning models. Here is a complete list of forecasting methods in this article:

• AutoARIMA
• Prophet
• NeuralProphet
• Random Forest
• XGBoost
• Mixture of Experts
• N-BEATS

Along the way, I compared accuracy, interpretability, and deployment feasibility — not as an academic exercise, but to answer a practical question: which forecasting tools can deliver the kind of reliable, actionable climate predictions that help data centers optimize cooling, lower energy costs, and conserve water?

In addition, every forecast plot will include a prediction interval, not just a single forecast line. A lone line can be misleading, as it implies, we “know” the exact humidity level on a future day. Since the weather is never certain, operators need more than a single forecast. A prediction interval gives a range of likely humidity values, reflecting both model limits and natural variability.

Confidence intervals tell us about the mean forecast. Prediction intervals are broader — they cover where real humidity readings might fall. For operators, that difference is key: underestimate the range and you risk overheating; overestimate it and you spend more than you need.

A good way to judge prediction intervals is by coverage. With a 95% confidence interval, we expect about 95 out of 100 points to fall within it. If only 86 do, the model is too sure of itself. Conformal prediction adjusts the range so the coverage lines up with what was promised.

Conformal prediction takes the model’s past errors (residuals = actual − predicted), finds a typical error size (quantile of those residuals), and adds it around each new forecast to create an interval that covers the true value with the desired probability.

Here is the main algorithm for the computation of the prediction interval:

1. Create a calibration set.
2. Compute the residuals:

where the first term on the right side of the equation is the actual observed value, and the second term is the model prediction for the same point.

3. Find the quantile of residuals:

where alpha is the significance level, e.g. 0.05.

4. Form the conformal interval for a new forecast:

The interval at time t is equal to:

3. Data and Forecasting Methods (with Code)

The code for all forecasting methods discussed in this article is on Github. The directory link is at the end of the article. Before we discuss our forecasting methods, let us take a look at our data. Figure 1 shows the training data, and Figure 2 shows the test data. As seen in Figure 1, the training data behave in a stable, stationary manner. Yet Figure 2 tells a different story: the test period breaks that stability with a clear downward drift. This stark contrast raises the stakes.

We expect that structure-based methods, such as ARIMA, and traditional ML methods, such as Random Forest, will have a hard time capturing the downward shift because they are not temporally aware. On the other hand, deep learning forecasting methods can understand that the test series mirrors similar seasonal segments within the training data, and therefore are more equipped to capture the downward shift.

Figure 1. Humidity Training Data Figure 2. Test Humidity Data

3. A. AutoARIMA Forecasting

ARIMA (AutoRegressive Integrated Moving Average) models combine three elements:

• AR terms that capture the memory of past values
• MA terms that account for past forecasting errors
• Differencing (the “I”) to remove trends and make the series stationary.

3. A. 1. AutoARIMA Test Data Forecast

Traditionally, the analyst must test for stationarity and decide how much differencing to apply before fitting the model. This is a difficult process that can also be prone to error. AutoARIMA removes that burden by running statistical tests under the hood. It automatically decides the degree of differencing and searches across AR and MA combinations to select the best fit based on information criteria. In short, you can hand it raw, non-stationary data, and it will handle the detective work for you—making it both powerful and simple.

Figure 3 shows the AutoARIMA forecast (orange dashed line) and the prediction interval (yellow shaded area). ARIMA can follow short-term fluctuations but is unable to capture the longer downward trend; therefore, the forecast becomes a steady line. This is a typical limitation: ARIMA can capture local autocorrelation, but it cannot capture evolving dynamics. The widening prediction intervals make sense—they reflect growing uncertainty over time.

**Figure 3. AutoARIMA forecast of the test data, with prediction interval.

3. A. 2. Accuracy of *AutoARIMA *and Coverage of Prediction Interval

MSE	RMSE	MAE
398.19	19.95	15.37

Table 1. Errors of AutoARIMA

In Table 1, we report three different errors: MSE, RMSE, and MAE to provide a complete picture of model accuracy. RMSE and MAE are the easiest to read, since they use the same units as the target. RMSE puts more weight on big misses, while MAE tells you the average size of an error. We also report MSE, which is less intuitive but commonly used for comparison.

Regarding the prediction interval, we did not apply conformal prediction, since ARIMA already returns model-based 95% prediction intervals. These intervals are derived from *ARIMA’*s statistical assumptions rather than from the model-agnostic conformal prediction framework. However, not using conformal prediction yielded an imperfect *coverage *of the prediction interval (85.96%).

3. A. 3. Interpretability of AutoARIMA

One of the appealing aspects of AutoARIMA is how easy it is to “see” what the model is doing. Figure 4 depicts the partial autocorrelation function (PACF), which computes the partial correlation of a stationary time series with lagged values of itself. This Figure shows that today’s humidity still “remembers” yesterday and the days before, with correlations fading over time. This lingering memory is exactly what ARIMA uses to build its forecasts.

Figure 4. PACF plot

Additionally, we ran the *KPSS *test, which confirmed that the train data is indeed stationary.

3. A. 4. Mode of Deployment

AutoARIMA** is easy to deploy: once given a time series, it automatically selects orders and fits without manual tuning. Its light computational footprint makes it practical for batch forecasting and even for deployment on edge devices with limited resources. However, its simplicity means it is best suited for stable environments rather than settings with abrupt structural changes. **

3. B. *Prophet *Forecasting

In this section,* we will discuss Prophet, *an open forecasting library originally developed by Facebook (now Meta). Prophet treats a time series as the sum of three key pieces: a trend, seasonality, and holidays or special events:

• Trend: The trend is modeled flexibly with either a straight line that can bend at change-points or a saturating growth curve, which rises quickly and then flattens out. This is like the cooling demand in a data center that grows with workloads but eventually levels off once the system reaches capacity.
• Seasonality is captured with smooth Fourier terms, so recurring patterns such as weekly or yearly cycles are learned automatically.
• Holidays or events can be added as regressors to explain one-off spikes.

Therefore, we see that Prophet has a very convenient additive structure. This makes *Prophet *easy to understand and robust to messy real-world data.

Code Snippet 1 below shows how to train and fit the *Prophet *model and use it to forecast the test data. Note that the Prophet forecast returns yhat_lower and yhat_upper, which are the limits of the prediction interval, and sets the prediction interval to 95% (line 1 of code). So, like AutoARIMA above, the prediction interval is not derived from conformal prediction.

#Train and Fit the Prophet Model
model = Prophet(interval_width=0.95)
model.fit(train_df)
#Forecast on Test Data
future = test_df[['ds']].copy()
forecast = model.predict(future)
cols = ['ds', 'yhat', 'yhat_lower', 'yhat_upper']
forecast_sub = forecast[cols]
y_true = test_df['y'].to_numpy()
yhat       = forecast['yhat'].to_numpy()
yhat_lower = forecast['yhat_lower'].to_numpy()
yhat_upper = forecast['yhat_upper'].to_numpy()

Code Snippet 1. Training and Forecasting with Prophet

3. B. 1. Prophet Test Data Forecast

Figure 5 shows *Prophet’*s forecasting of the test data (the orange line) and the prediction interval (blue shaded area). In contrast to AutoArima, we can see that *Prophet’*s forecast captures well the downward trend of the data.

Figure 5. Prophet test data forecasting with prediction interval.

3. B. 2. Prophet Accuracy and Prediction Interval Coverage

MSE	RMSE	MAE
105.26	10.25	8.28

Table 2. Prophet errors.

The forecasting improvement of *Prophet *in comparison to *AutoARIMA *can be also seen in Table 2 above, which depicts the errors.

As we said above, the prediction interval was not derived using conformal prediction. However, in contrast to AutoARIMA, the prediction interval *coverage *is much better: 93.86%.

3. B. 3. *Prophet *Interpretability

As we said above**, ***Prophet *is transparently additive: it decomposes the forecast into trend, smooth seasonalities, and optional holiday/regressor effects, so component plots show exactly how each piece contributes to *yhat *and how much each driver moves the forecast.

Figure 6. Prophet forecast components.

Figure 6 above shows the *Prophet *forecast components: a gentle downward trend over time (top), a weekly cycle where weekends are more humid and mid-week is drier (middle), and a yearly cycle with humid winters, a dip in spring, and rising values again in summer and fall (bottom).

3. B. 4. Prophet Mode of Deployment

Prophet is simple to deploy, runs efficiently on standard CPUs, and can be used at scale or on edge devices, making it well-suited for business applications that need quick, interpretable forecasts.

3. C. Forecasting With NeuralProphet

NeuralProphet** **is a neural-network-based extension of Prophet. It keeps the same core structure (trend + seasonality + events) but adds:

• A feed-forward neural network to capture more complex, nonlinear patterns.
• Support for lagged regressors and autoregression (can use past values directly, like AR models).
• The ability to learn multiple seasonalities and higher-order interactions more flexibly.

Prophet** **has the great characteristics of being statistical and additive, which enable transparency and quick forecasts. NeuralProphet builds on that framework but brings in deep learning. *NeuralProphet *can pick up nonlinear and autoregressive effects, but that extra flexibility makes it harder to interpret.

As Code Snippet 2 below shows, we used seasonality in our model to exploit the seasonal mode of humidity.

model = NeuralProphet(
seasonality_mode='additive',
yearly_seasonality=False,
weekly_seasonality=False,
daily_seasonality=False,
n_changepoints=10,
quantiles=[0.025, 0.975]  # For 95% prediction interval
)
# Add custom seasonality (~6 months)
model.add_seasonality(name='six_month', period=180, fourier_order=5)
model.fit(train, freq='D', progress='bar')
future=model.make_future_dataframe(train,periods=len(test), n_historic_predictions=len(train))
forecast = model.predict(future)

Code Snippet 2. Training and forecasting with NeuralProphet

3. C. 1. *NeuralProphet *Test Data Forecast

Figure 7 shows *NeuralProphet’s *forecasting (the dashed green line) and the prediction interval (light green shaded area). Similar to Prophet, *NeuralProphet’s *forecast captures well the downward trend of the data.

Figure 7. NeuralProphet forecasting of test data with a prediction interval.

3. C. 2. NeuralProphet Accuracy and Prediction Interval Coverage

MSE	RMSE	MAE
145.31	12.05	9.64

Table 3. NeuralProphet errors.

It is interesting to note that, despite neural augmentation and the addition of seasonality, NeuralProphet’s errors are slightly higher than Prophet’s. **NeuralProphet adds more moving parts, but that doesn’t always translate into better forecasts. On limited or messy data, its extra flexibility can actually work against it, while Prophet’s simpler setup often keeps the predictions steadier and a bit more accurate.

Regarding the precision interval, it is drawn using the limit variables, yhat1 2.5 and yhat1 97.5, returned by NeuralProphet. The coverage of the 95% prediction interval is 83.33%. This is low, but it is expected because it is not computed using conformal prediction.

3. C. 3. NeuralProphet Interpretability

The three panels in Figure 8 below show, respectively:

• Panel 1. Trend: Shows the learned baseline level and where the slope changes (changepoints) in the piecewise-linear trend.
• Panel 2.** Trend rate change:** Bars/spikes indicating how much the trend’s slope jumps at each changepoint (positive = faster growth, negative = slowdown/downturn).
• Panel 3.** Seasonality:** The one-period shape/strength of the seasonal component. Figure 8. These three panels show the learned trend baseline, trend rate changes, and 6-month seasonality estimated by the model. These highlight how NeuralProphet detects shifts in slope and overall change dynamics.

3. C. 4. *NeuralProphet *Mode of Deployment

NeuralProphet runs well on CPUs and can be used in scheduled jobs or small APIs. While heavier than Prophet, it’s still practical for most containerized or batch deployments, and can also run on edge devices like a Raspberry Pi with some setup.

3. D. Random Forest Forecasting

Random Forest is a machine learning technique that can also be used for forecasting. This is achieved by turning past values and external factors into features. This is how it works: First, it builds multiple decision trees on randomly selected parts of the data. Then, it averages their results. This helps avoid overfitting and capture nonlinear patterns.

3. D. 1. Random Forest Forecast

Figure 9 below shows the Random Forest forecast (orange line) and the prediction interval (the blue shaded area). We can see that Random Forest does not perform as well. This happens because Random Forest doesn’t really “understand” time. Instead of following the natural sequence of the data, it just looks at lagged values as if they were ordinary features. This makes the model good at capturing some nonlinear patterns but weak at recognizing longer trends or shifts over time. The result is forecasts that look overly smooth and less accurate, which explains the higher MSE.

Figure 9. Random Forest forecast of test data with precision interval.

3. D. 2. Random Forest Accuracy and Precision Interval

MSE	RMSE	MAE
448.77	21.18	17.6

Table 4. Random Forest Errors

The poor performance of Random Forest is also evident in the high error values shown in Table 4 above.

Regarding the prediction interval, this is the first forecasting technique where we used conformal prediction to compute the prediction interval.

The coverage of the prediction interval was estimated to be an impressive 100%.

3. D. 3. *Random Forest *Interpretability

Figure 10. Random Forest Lag Importance

Random Forest provides some interpretability by ranking the importance of the features used in its predictions. In time-series forecasting, this often means examining which lags of the target variable contribute most to the model’s predictions. The feature importance plot in Figure 10 above shows that the very recent lag (one day back) dominates, carrying nearly 80% of the predictive weight, while all longer lags contribute almost nothing. This indicates that the Random Forest relies heavily on the immediate past value to make forecasts, smoothing over longer-term dependencies. While such interpretability helps us understand what the model is “looking at,” it also highlights why Random Forest may underperform in capturing broader temporal dynamics compared to methods better suited to sequential structure.

3. D.4. Random Forest Mode of Deployment

Random Forest models are relatively lightweight to deploy, since they consist of a set of decision trees and require no special hardware or complex runtime. They can be exported and run efficiently on standard servers, embedded systems, or even edge devices with limited “compute”, making them practical for real-time applications where resources are constrained. However, their memory footprint can grow when many trees are used, so compact versions or tree pruning can be applied in edge environments.

3. E. XGBoost Forecasting

XGBoost** **is a boosting algorithm that builds trees one after another, with each new tree correcting the mistakes of previous trees. In forecasting, we provide it with features such as lagged values, rolling averages, and external variables, allowing it to learn time patterns and relationships between variables. It works well because it incorporates strong regularization, which enables it to handle large and complex datasets more effectively than simpler methods. But, like Random Forests, it doesn’t naturally handle time order, so its success depends heavily on how well the time-based features are designed.

3. E. 1. XGBoost Test Data Forecast

Figure 11 shows the XGBoost forecast (orange line) and the prediction interval (blue shaded area). We can see that the forecast closely follows the humidity signal and is therefore very successful at predicting humidity. This can also be confirmed in Table 5 below, which depicts relatively small errors, particularly in comparison to Random Forest.

Figure 11. XGBoost forecasting of test data.

XGBoost builds trees sequentially, and this is the source of its strength. As we previously said, each new tree corrects the mistakes of the previous ones. This boosting process is combined with strong regularization. This method can pick up quick changes, deal with tricky patterns, and still stay reliable. That usually makes its forecasts closer to reality than those of Random Forest.

3. E. 2. XGBoost Forecasting Accuracy and Prediction Interval Coverage

MSE	RMSE	MAE
57.46	7.58	5.69

Table 5. XGBoost forecasting errors.

Here, we also used conformal prediction for the computation of the prediction interval. For this reason, the precision interval coverage is high: 94.74%

3. E. 3. XGBoost Forecasting Interpretability

XGBoost, despite its complexity, remains fairly interpretable compared to deep learning models. It provides feature importance scores that show which lagged values or external variables drive the forecasts. We can look at feature importance plots, much like with Random Forest. For a deeper view, SHAP values show how each factor influenced a single prediction. This gives both an overall picture and case-by-case insight.

Figure 12 below shows the weight of a feature, e.g. how often it is used in splits.

**Figure 12. XGBoost lag importance.

The series below shows the gain for each lag, i.e., the average improvement when a lag is used.

{‘humidity_lag_1’: 3431.917724609375, ‘humidity_lag_2’: 100.19515228271484, ‘humidity_lag_3’: 130.51077270507812, ‘humidity_lag_4’: 118.07515716552734, ‘humidity_lag_5’: 155.8759307861328, ‘humidity_lag_6’: 152.50379943847656, ‘humidity_lag_7’: 139.58169555664062}

Figure 13. SHAP values for XGBoost lags.

The SHAP summary plot in Figure 13 shows that humidity_lag_1 is by far the most influential feature, with high recent humidity values pushing forecasts upward and low recent humidity values pulling them downward. Later lags (2–7) play only a minor role, indicating the model relies mainly on the most recent observation to make predictions.

3. E. 4. XGBoost Mode of Deployment

*XGBoost *is also straightforward to deploy across platforms, from cloud services to embedded systems. Its main advantage over Random Forest is efficiency: models are typically smaller and faster at inference. This makes the model practical for real-time use. Its support across many languages and platforms makes it easy to implement in various settings.

3. F. Mixture of Experts (MoE) Forecasting

The MoE approach combines several specialized models (“experts”), each tuned to capture different aspects of the data, with a gating network that determines the weight each expert should have in the final forecast.

In Code Snippet 3, we see the keywords AutoGluon and Chronos. Let us explain what they are: We implemented the Mixture of Experts using Hugging Face models integrated through AutoGluon, with *Chronos *serving as one of the experts. Chronos is a family of time-series forecasting models built using transformers. *AutoGluon *is a helpful AutoML framework that can handle tabular, text, image, and time series data. Mixture of Experts is just one of its many strategies to boost performance using model ensembling.

from autogluon.timeseries import TimeSeriesDataFrame, TimeSeriesPredictor
MODEL_REPO = "autogluon/chronos-bolt-small"
LOCAL_MODEL_DIR = "models/chronos-bolt-small
predictor_roll = TimeSeriesPredictor(
prediction_length=1,
target="humidity",
freq=FREQ,
eval_metric="MSE",
verbosity=1
)
predictor_roll.fit(train_data=train_tsd, hyperparameters=hyperparams, time_limit=None)

Code Snippet 3: Fitting the Autogluon model TimeSeriesPredictor

In Code Snippet 3 above, the predictor is called predictor_roll because *MoE *forecasting generates predictions in a rolling fashion: each forecasted value is fed back into the model to predict the next step. This approach reflects the sequential nature of time series data. It also allows the gating network to dynamically adjust which experts it relies on at each point in the horizon. Rolling forecasts also expose how errors accumulate over time. This way, we achieve a more realistic view of multi-step performance.

3. F. 1. MOE Test Data Forecast

Figure 14. MOE test data forecasting and prediction interval.

As shown in Figure 14 above, MoE performs extremely well and closely follows the actual test data. As Table 6 below shows, MoE achieves the best accuracy and the smallest errors overall.

3. F. 2. MOE Forecasting Accuracy and Prediction Interval Coverage

MSE	RMSE	MAE
45.52	6.75	5.18

Table 6. Mixture of Experts Forecasting Errors.

The coverage of the 95% prediction interval is extremely good (97.37%) because we used conformal prediction.

3. F. 3. *MOE *Forecasting Interpretability

There are several ways to gain insight into how MoE works:

• Gating network weights: By inspecting the gating network’s outputs, you can see which expert(s) were given the most weight for each prediction. This reveals when and why certain experts are trusted more.
• Expert specialization: Each expert can be analyzed separately—e.g., one may capture short-term fluctuations while another handles longer seasonal trends. Looking at their forecasts side by side helps explain the ensemble’s behavior.
• Feature attribution (SHAP/feature importance): If the experts are themselves interpretable models (like trees), their feature importances can be computed. Even for neural experts, we can use SHAP or integrated gradients to understand how features influence decisions.

So while MoE is not as “out-of-the-box interpretable” as *Random **Forest *or XGBoost, you can open the black box by analyzing which expert was chosen when, and why.

3. F. 4. MoE Mode of Deployment

Deploying Mixture of Experts is more demanding than tree ensembles. The reason is that it involves both the expert models and the gating network. In data centers, on servers, or in the cloud, implementation is straightforward because modern frameworks like PyTorch and TensorFlow can easily handle orchestration. For edge devices, however, deployment is much more difficult. The specific challenges are the complexity and size of MoE. Therefore, pruning, quantization, or limiting the number of active experts is often necessary to keep inference lightweight. *AutoML *frameworks such as AutoGluon simplify deployment by wrapping the entire MoE pipeline. The Hugging Face site also hosts large-scale *MoE *models that can help us scale up to production-grade AI systems.

3. G. N-BEATS Forecasting

N-BEATS [9] is a deep learning model for time series forecasting built from stacks of fully connected layers grouped into blocks. Each block outputs a forecast and a backcast, with the backcast removed from the input so the next block can focus on what remains. By chaining blocks, the model gradually refines its predictions and captures complex patterns. In our implementation, we used a sliding-window setup: the model examines a fixed window of past observations (and external drivers, such as mean temperature) and learns to predict several future points simultaneously. The window then shifts forward step by step across the data, giving the model many overlapping training examples and helping it generalize to unseen horizons.

In this article, N-BEATS was implemented using N-BEATSx, which is an extension of the original N-BEATS architecture that includes exogenous drivers. N-BEATS and *N-BEATSx *are part of the *NeuralForecast *library [10], which offers several neural forecasting models. As can be seen in Code Snippet 4, N-BEATS was set up using a factory function (make_model), which lets us define the forecast horizon variable and add mean temperature (meantemp) as an extra input. The idea behind including meantemp is straightforward: the model doesn’t just learn from past values of the target series, but also from this key outside factor.

def make_model(horizon):
return NBEATSx(
input_size=INPUT_SIZE,
h=horizon,
max_steps=MAX_STEPS,
learning_rate=LR,
stack_types=['seasonality','trend'],
n_blocks=[3,3],
futr_exog_list=['meantemp'],
random_seed=SEED,
# early_stop_patience=10,  # optional
)
# Fit model on train_main
model_cal = make_model(horizon=CAL_SIZE)
nf_cal = NeuralForecast(models=[model_cal], freq='D')

Code Snippet 4: N-BEATS model creation and fitting.

3. G. 1. N-BEATS Test Data Forecast

Figure 15 shows the N-BEATS forecasting model (orange line) and the prediction interval (blue area). We can see that the forecast is able to follow the downward trend of the data, but stays above the data line for a significant portion of the data.

Figure 15. N-BEATS forecast of the test data and prediction interval.

3. G. 2. N-BEATS Accuracy and Prediction Interval Coverage

MSE	RMSE	MAE
166.76	12.91	10.32

Table 7. N-BEATS forecasting errors.

For N-Beats, we used conformal prediction, and, as a result, the prediction interval coverage is excellent: 98.25%

3. G. 3. N-BEATS Interpretability

In our experiments, we used the generic form of N-BEATS, which treats the model as a black-box forecaster. However, N-BEATS also offers another architecture with “interpretable blocks” that explicitly model trend and seasonality components. This means the network not only produces accurate forecasts but can also decompose the time series into human-readable parts, making it easier to understand what drives the predictions.

3. G. 4. N-BEATS Mode of Deployment

Because N-BEATS is built entirely from feed-forward layers, it is relatively lightweight compared to other deep learning models. This makes it straightforward to deploy not only on servers but also on edge devices, where it can deliver multi-step forecasts in real time without heavy hardware requirements.

Conclusion

In this article, we compared several forecasting approaches—from classical baselines such as *AutoARIMA *and *Prophet *to machine-learning methods such as XGBoost and deep learning architectures such as N-BEATS and *Mixture of Experts. *Simpler models offered transparency and easy deployment but struggled to capture the complexity of the humidity series. In contrast, modern deep learning and ensemble-based approaches significantly improved accuracy, with the Mixture of Experts achieving the lowest error (MSE = 45). T

Below we see a summary of the mean square errors:

• AutoARIMA MSE = 398.19
• *Prophet *MSE = 105.26
• NeuralProphet MSE = 145.31
• Random Forest MSE = 448.77
• *XGBoost *MSE = 57.46
• *Mixture of Experts *MSE = 45.52
• N-BEATS MSE = 166.76

Besides accuracy, we also computed a prediction interval for each forecasting method and demonstrated the use of conformal prediction to compute an accurate prediction interval. The conformal prediction code for each forecasting method can be found in my Jupyter notebooks on Github. Prediction intervals are important because they give a realistic sense of forecast uncertainty.

For each forecasting method, we also examined its interpretability and mode of deployment. With models like AutoARIMA and Prophet, interpretation comes straight from their structure. *AutoARIMA *shows how past values and errors influence the present, while Prophet splits the series into components like trend and seasonality that can be plotted and examined. Deep learning models such as N-BEATS or Mixture of Experts act more like black boxes. However, in their case, we can use tools such as SHAP or error analysis to get insights.

Deployment is also important: lighter models, such as XGBoost, can run efficiently on edge devices. Larger deep learning models can utilize frameworks such as AutoGluon to streamline their training. A great benefit is that these models can be deployed locally to avoid API limits.

In conclusion, our results show that reliable humidity forecasts are both possible and useful for day-to-day data center operations. By adopting these methods, data center operators can expect energy demand peaks and optimize cooling schedules. This way, they can reduce both energy consumption and water use. Given that AI power demands constantly rise, the ability to forecast environmental drivers, such as humidity, is crucial because it can make digital infrastructure more resilient and sustainable.

Thank you for reading!

The entire code of the article can be found at:

https://github.com/theomitsa/Humidity_forecasting

References

[1] J. O’ Donnell, and C. Crownhart, We Did the Math on AI’s Energy Footprint. Here’s The Story You Haven’t Heard (2025), MIT Technology Review.

[2] Staff writers, Inside the Relentless Race for AI Capacity (2025), Financial Times, https://ig.ft.com/ai-data-centres/

[3] P. Li, et al, Making AI Less Thirsty: Uncovering and Addressing the Water Footprint of AI Models (2025), Communications of the ACM, https://cacm.acm.org/sustainability-and-computing/making-ai-less-thirsty/

[4] Jackson Mechanical Service Blog, Managing Humidity Levels: A Key Factor For Data Center Efficiency and Uptime (2025), https://www.jmsokc.com/blog/managing-humidity-levels-a-key-factor-for-data-center-efficiency-and-uptime/#:~:text=Inadequate%20management%20of%20humidity%20within,together%20might%20precipitate%20revenue%20declines.

[5] D. Genkina, Is It Lunacy to Put a Data Center on the Moon? (2025), IEEE Spectrum.

[6] R. Burkett, Lunar Data Center Intact Despite Lunar Lander’s Botched Landing, St. Pete Company Says (2025), https://www.fox13news.com/news/lunar-data-center-intact-despite-lunar-landers-botched-landing-st-pete-company-says

[7] Data Centers in Delhi, https://www.datacenters.com/locations/india/delhi/delhi

[8] Staff writers, Delhi Developer to Invest $2 Billion on India Darta Centre Boom (2025), Economic Times of India Times, https://economictimes.indiatimes.com/tech/technology/delhi-developer-to-invest-2-billion-on-india-data-centre-boom/articleshow/122156065.cms?from=mdr

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[10] NeuralForecast Library, https://github.com/Nixtla/neuralforecast?tab=readme-ov-file

Footnote:

1. All images/figures are by the author, unless otherwise noted.
2. Link to data used for forecasting in this article: https://www.kaggle.com/datasets/sumanthvrao/daily-climate-time-series-data/data
3. Data License: The data has a Creative Commons License:** CC0 1.0**. Link to data license: https://creativecommons.org/publicdomain/zero/1.0/

Excerpt from license deed mentioning commercial use: You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.