Prediction of HVAC loads at diﬀerent spatial resolutions
and buildings using deep learning models
Antonio Liguori1,∗, Shiying Yang1,∗, Romana Markovic2, Thi Thu Ha Dam1,
J´erˆome Frisch1, Andreas Wagner2, Christoph van Treeck1
1E3D - Institute of Energy Eﬃciency and Sustainable Building,
RWTH Aachen University, Aachen, Germany
2Karlsruhe Institute of Technology, Karlsruhe, Germany
∗Equal contribution, corresponding author: email@example.com
This paper explores the applicability of deep learning-
driven models for the prediction of energy consump-
tion in generic commercial buildings. The modeling
approach relies on recurrent neural networks (RNNs),
while the input consists of physical data streams such
as indoor air temperature in diﬀerent thermal zones
and data obtained from the central heating ventila-
tion and air conditioning (HVAC) system. The re-
search steps include the implementation of an exist-
ing RNN-based model for energy consumption and
further model optimization using training and vali-
dation sets. The ﬁnal model was evaluated using the
data from two datasets. Additionally, the evaluation
performance was tested in case of the varied spatial
and system granularities. The results showed that
the optimal model architecture was dataset-agnostic.
The results showed that predicting the HVAC energy
consumption is more challenging at the higher spa-
tial granularity, when compared to building wise or
multi-zone wise modeling.
Exploring the impact of the spatial granularity on the
predictive performance of data-driven HVAC energy
consumption models in commercial buildings.
The practical implications of this work can be sum-
marized as follows:
•Applicability of the model to diﬀerent energy
consumption data sets with no tuning and cal-
•Adaptation of the model to the day-ahead esti-
mation of energy consumption data for a better
load scheduling and an increased use of renew-
able energy sources.
The European policies identiﬁed energy consumption
in buildings as one of the key goals by 2020 and be-
yond (D’Agostino et al. (2017), P´erez-Lombard et al.
(2008)). In both residential and commercial build-
ings, a signiﬁcant proportion of energy is consumed
for HVAC systems (P´erez-Lombard et al. (2008)).
At the same time, HVAC systems have the largest
energy-saving potential, ranging between 15-30% for
commercial buildings (P´erez-Lombard et al. (2008),
Li and Wen (2014)).
The buildings’ energy saving potential can be fulﬁlled
by two mechanisms. The ﬁrst approach relies on the
improvements in technical equipment and more ef-
ﬁcient building operation. Additionally, the second
approach focuses on a better use of the renewable
energy, while considering the ﬂuctuating nature of
renewable energy sources and challenges related to
energy storage. In summary, both latter mechanisms
for improving energy eﬃciency require reliable pre-
diction of the building’s energy consumption. Here,
data-driven models can be seen as a promising tool.
This motivated a number of studies on data-
driven modeling of energy consumption (Kusiak
et al. (2010), Maasoumy and Sangiovanni-Vincentelli
(2012), Ahmad et al. (2017), Capozzoli et al. (2017),
Markovic et al. (2020), Koschwitz et al. (2018)). Ku-
siak et al. (2010) used a data-driven approach to
minimize the energy usage of air-conditioning in an
oﬃce-type facility, while Maasoumy and Sangiovanni-
Vincentelli (2012) presents a hierarchical control
strategy model to balance comfort and energy con-
sumption with a reduction in HVAC energy consump-
tion. Niu et al. (2018) made use of diﬀerent data-
driven algorithms to estimate HVAC related elec-
tricity consumption in a university dormitory while
O’Neill and O’Neill (2016) created a data-driven ap-
proach using probabilistic graphical theory to predict
building energy performance.
In order to predict total energy consumption of a
building, Li et al. (2017) combined stacked autoen-
coders (SAEs) with the extreme learning machine
(ELM) to beneﬁt from both approaches. Sendra-
Arranz and Guti´errez (2020) developed several long-
short-term memory (LSTM)-based models to predict
the next day energy consumption of a self suﬃcient
solar house in Madrid, based on the previous day
of measurements. Ben-Nakhi and Mahmoud (2004)
used general regression neural networks (GRNNs) to
predict hourly cooling load for three oﬃce build-
ings, while Azadeh et al. (2008), Gonzalez and Za-
marreno (2005), Kim and Cho (2019) and Nizami
and Al-Garni (1995) predicted electric energy con-
sumption using feedforward neural networks. After
achieving accuracy with multi-layer perceptron with-
out transformed variables for estimating energy de-
mand, Pino-Mej´ıas et al. (2017) concluded that the
neural networks are more suitable for combined heat-
ing and cooling energy consumption modeling, when
compared to statistical regression models. When con-
sidering plug loads Markovic et al. (2020) and Zheng
et al. (2019) developed a LSTM model intending to
predict competitively accurate miscellaneous electric
loads (MELs). The results showed that it outper-
formed all other existing MEL models using identical
data sets obtained from commercial buildings, while
Zheng et al. (2019) conﬁrmed that the LSTM archi-
tectures are as well suitable for MEL modeling in res-
idential settings. Wang et al. (2019) also made use of
an LSTM model to predict plug loads and achieved
among linear regression models and traditional arti-
ﬁcial neural networks an improvement in prediction
Grouping diﬀerent rooms of a building that share
similar characteristics (e.g. orientation, occupancy)
into diﬀerent thermal zones is a commonly adopted
approach in building performance simulation and it
was conﬁrmed that the right formulation of thermal
multi-zone models can, indeed, lead to lower com-
putational costs without aﬀecting the accuracy of
the building simulation (van Treeck (2010)). On the
other side, whether the inﬂuence of varied time res-
olutions has been already evaluated for some appli-
cations (Markovic et al. (2019); Zheng et al. (2019);
Jain et al. (2014)), an analysis of the impact of spa-
tial granularity, i.e. level of aggregation of data, on
the performance of data-driven models is worth fur-
ther investigation. Since there is no generally ac-
cepted deﬁnition of spatial granularity (Pozzani and
Zim´anyi (2010)) or spatial resolution, in this con-
text the terms refer to the monitoring of data in a
much more detailed way, such as for a large num-
ber of zones or from a building aggregated to a ﬂoor
aggregated scenario. In this respect there is a re-
quirement to keep the practicality and accuracy in
balance (Chong et al. (2021)), because of the many
levels of spatial granularity. In the scope of an early
study, Kalogirou et al. (1997) applied neural networks
to predict space heating loads for spatial granular-
ity varying from small rooms to large spaces of an
educational building in Cyprus. The results proved
that the performance of the proposed model could be
improved by grouping the input data into two dif-
ferent zones. However, due to the lack of historical
data, the inputs consisted mostly of geometrical pa-
rameters. Jain et al. (2014) proposed a sensor-based
forecasting model based on support vector regression
(SVR). This was applied to a multi-family residen-
tial building in New York City in order to estimate
the energy consumption at varied temporal and spa-
tial resolutions. In particular, the spatial resolution
was investigated at building, ﬂoor and unit levels. It
was demonstrated that the best model performance
could be achieved at ﬂoor level with hourly temporal
granularity. Finally, Zheng et al. (2019) studied the
accuracy of household electricity consumption predic-
tions at diﬀerent spatial granularity, using LSTM net-
works. The case study consisted of two households
with electricity consumption data aggregated at the
appliance and building-level. The results proved that
prediction accuracy could be higher if the whole en-
ergy consumption of the household was estimated at
the appliance-level (i.e. at the higher granularity).
The following knowledge was gained in the scope of
related existing studies:
•The deﬁned spatial resolution has a direct impact
on the goodness of energy consumption predic-
tion (Zheng et al., 2019; Markovic et al., 2020;
Kalogirou et al., 1997; Jain et al., 2014).
•The higher spatial resolution leads to better pre-
diction of MEL consumption in both residen-
tal and commercial settings (Zheng et al., 2019;
Markovic et al., 2020).
•In contrast to the MEL energy consumption,
the optimal HVAC energy consumption can be
predicted with higher accuracy when applied
to lower spatial granularities (Jain et al., 2014;
Kalogirou et al., 1997).
•RNNs and LSTMs neural networks are a suit-
able architecture for predicting both MEL
and HVAC energy consumption (Zheng et al.,
2019; Markovic et al., 2020; Sendra-Arranz and
•The energy use patterns in residential buildings
may diﬀer signiﬁcantly from the ones observed
in commercial buildings (Clevenger et al., 2014).
This work builds up on the existing knowledge re-
garding the suitable model architecture and explore
the impact of the spatial granularity on the HVAC
energy consumption in commercial buildings.
For that purpose, an existing RNN-based model was
implemented and evaluated using two independent
datasets. The original model was further developed
and evaluated using varied spatial data granularity,
from oﬃce wise data streams to large oﬃce buildings.
The remaining part of the paper is structured as fol-
lows: ﬁrst, the methodology and the experimental
setting is provided, including the description of the
datasets, optimization approach and evaluation met-
rics. Finally the results are presented and discussed
before the key ﬁndings are summarized.
Method and experimental setting
The next section provides the description of the
methodology, including datasets description, opti-
mization approach and evaluation metrics. The ap-
proach followed in this paper is based on the imple-
mentation and optimization of an existing deep learn-
ing model proposed by Chen et al. (2017). The earlier
method was re-implemented and evaluated for model-
ing HVAC loads at diﬀerent spatial resolutions, using
The ﬁrst dataset was generated using the software
Energy Plus and it was shared by the authors of
the original study (Chen et al. (2017)). The ana-
lyzed building was a 12-storey large oﬃce building
located in Seattle, USA, with a total ﬂoor area of
46,000 m2. It consisted of 55 input features, which
included zone-level measurements (e.g. indoor air
temperature, relative humidity), centralized HVAC
control and weather variables, recorded in the year
2004. Simulations were performed based on a time
discretization of 10 minutes.
The second dataset consisted of minute-wise moni-
toring data collected in a 3-ﬂoor oﬃce building lo-
cated in Aachen, Germany. The building had a to-
tal ﬂoor area of 7,500 m2with 73 single and dou-
ble occupied oﬃces (F¨utterer and Constantin (2014);
F¨utterer et al. (2013)). The data were collected dur-
ing the year 2014. The minute-wise collected moni-
toring data were down-sampled to a 10 minutes-based
frequency. For further information about the dataset
in question, the reader is referred to F¨utterer and
Constantin (2014); F¨utterer et al. (2013).
Implementation of existing RNN model
The original method proposed by Chen et al. (2017)
consisted of a RNN-based model used to estimate the
total electricity consumption of the previously de-
scribed building in Seattle. The model was ﬁrstly
implemented and validated in scope of a round-robin
study, and eventually the further optimization poten-
tial was explored.
The model was based on RNNs, which are typically
used to process sequential data (Goodfellow et al.
(2016)). The main diﬀerence with respect to classic
feed-forward conﬁgurations is that model’s parame-
ters can be shared among the input time-series, by
operating with a local memory used to store informa-
tion of the past sequence (Chen et al. (2017); Good-
fellow et al. (2016)).
All hyperparameters were ﬁxed as deﬁned in the orig-
inal study. The model’s architecture consisted of one
RNN layer, three feed-forward layers and an output
layer. A dropout is included in every feed-forward
layer with the value of 0.5. Since no information
about the learning rate were provided, it was set to
Analogously to the model development presented by
Chen et al. (2017), the training was performed by ran-
domly sampling 10 out of 12 months from the Seattle
dataset and by using the remaining 2 months for per-
formance evaluation. Since the hyperparameters were
ﬁxed as in the original study, no validation set from
the Seattle data was deﬁned. Additionally, electricity
consumption estimation was performed based on the
past 4 hours of input data, for each timestep.
Further model optimization
The previously described model was at ﬁrst tested us-
ing the data set collected in Aachen and ﬁnally fur-
ther optimized. Analogously to the setting used in
the previous steps, the model was further optimized
using a training and a validation set, while it was
tested using an evaluation set. Here, the validation
set was used to identify the optimal model hypothe-
sis, while the evaluation set was used to obtain the
ﬁnal performance on previously unseen data1. It was
investigated if the use of the longer input sequence
duration could lead to better performance and ex-
periments were conducted where the input sequence
was extended to six hours. Eventually 11 out of 12
months from the Seattle dataset were used as training
and validation sets, while the remaining one month
was used for evaluation. As loss function, the mean
squared error (MSE) was applied and it was mini-
mized using a stochastic gradient descendent (SGD)
optimizer with momentum.
In the second round of experiments, the model was
further optimized on the Aachen dataset, by conduct-
ing hyperparameter tuning using data from all ther-
mal zones from one building level. An overview of the
used features from the Aachen dataset is provided in
Table 1: Overview of the used features for the model
applied on the Aachen dataset.
Feature Unit of measure
Indoor air temperature °C
Set point temperatures °C
(two thermostats per oﬃce)
Indoor CO2concentration ppm
Indoor relative humidity %
“Day of the week” index -
Outdoor air temperature °C
Outdoor relative humidity %
Soil temperature over 5cm °C
Liquid precipitation mm
Average wind speed m/s
Wind direction deg
Atmospheric pressure mbar
Global radiation W/m2
Diﬀuse radiation W/m2
Thermal load kW
1For the formal deﬁnition of training, validation and test
sets, the reader is referred to Goodfellow et al. (2016).
The hyperparameter tuning was conducted on the
validation set and the selected optimal hyperparam-
eters are summarized in Table 2. The chosen compu-
tational environment consisted of Python 3.6.8, Ten-
sorﬂow 1.14.0 and Keras 2.2.0.
Since the total electricity consumption was not avail-
able in the second building, the target variables were
re-deﬁned as heating and cooling loads. This resulted
in two diﬀerent model’s formulations, namely winter
(W) and summer (S) mode. For both cases, 11 out
of 12 months were used as training and validation
sets, while the remaining month (May and Novem-
ber for summer and winter mode, respectively) was
used as evaluation. The deﬁned data split for each
target variable from the Aachen dataset is presented
in Figure 1.
Table 2: Hyperparameter search results.
Batch size 200
RNN hidden units 128
RNN hidden layers 1
Feed-forward hidden units 64
Feed-forward hidden layers 3
Learning rate 0.1
Dropout rate 0
1 2 3 4 5 6 7 8 9 10 11 12
Training Set Validation Set
Figure 1: Training, validation and evaluation data
split (winter and summer mode) for each spatial gran-
In addition to exploring the model’s generalization to
diﬀerent target functions, such as total energy con-
sumption, heating energy consumption and cooling
energy consumption, the applicability of the model
was tested for diﬀerent spatial resolutions. In partic-
ular, the model was retrained using data that were
aggregated at varied spatial granularity, as in Figure
1. The explored cases included oﬃce-wise, ﬂoor-wise
and building-wise conﬁgurations.
The performance of the proposed method was as-
sessed by using the root mean squared error (RMSE),
the mean absolute error (MAE), the normalized root
mean squared error (NRMSE) and the coeﬃcient of
determination (R2), as formulated by Willmott and
Matsuura (2005) and Hahn (1973). The RMSE was
chosen as the main accuracy indicator, being the es-
tablished evaluation metric by the related research
(Willmott and Matsuura (2005)) and was deﬁned as
Nonetheless, the RMSE alone does not provide suf-
ﬁcient information, neither about the total average
error nor about its variability along the predictive
horizon (Willmott and Matsuura (2005)) and it is
therefore used as a ﬁrst comparison with models used
in other studies. In order to account for the ambigu-
ity of information from the RMSE, it was opted for
a further absolute indicator, namely MAE (Willmott
and Matsuura (2005)), formulated as:
A comparison between varied spatial resolution con-
ﬁgurations was made by means of normalized metrics
(i.e. NRMSE and R2), deﬁned as:
NRM SE =RMSE
R2= 1 −Pn
iis the real output value, Xpred
predicted output value, Xobs
mean is the average of the
real output values, Xobs
max is the maximum real out-
put value, Xobs
min is the minimum real output value
and nis the total number of output values. Due to
the stochastic initialization of the model’s weights, it
was decided to run the evaluations 10 times and to
weight the earlier metrics accordingly.
Round robin evaluation of existing model
The obtained model’s performance in terms of
NRMSE was in the same range as in the study earlier
presented by Chen et al. (2017). The originally con-
ﬁrmed NRMSE of 0.078 could be reproduced with a
small diﬀerence and the NRMSE obtain in this round
robin study was 0.05. Additionally, performance was
quantiﬁed using further metrics that include MAE,
RMSE and R2and the results are presented in Ta-
ble 3. Finally, the simulated and measured electricity
consumption trends shown in Figure 2 conﬁrmed that
the model could accurately forecast the energy values
along all the test set.
Table 3: Round-robin study performance obtained on
the dataset from the building in Seattle.
MAE RMSE NRMSE R2
[MJ] [MJ] [-] [-]
Tot 37.71 45.55 0.05 0.97
Figure 2: Monthly course of simulated and measured
electricity consumption for the whole Seattle dataset.
Model evaluation using an independent
Table 4 summarizes the performance of the proposed
method for estimating the HVAC energy consumption
using the data collected in Aachen in the case of sum-
mer (S) and winter (W) mode, while the predicted
and measured energy consumption are presented in
Figure 3. It can be observed that the model was
able to capture the total building’s energy demand for
both heating and cooling, showing no signiﬁcant per-
formance drop in forecasting the two variables. This
is also conﬁrmed by the high R2values, which indi-
cate a relatively accurate ﬁtting of the real thermal
Table 4: Model performance on the whole Aachen
MAE RMSE NRMSE R2
[kW] [kW] [-] [-]
S 4.56 5.79 0.07 0.92
W 2.94 3.87 0.06 0.88
Figure 3: Monthly course of simulated and measured
thermal loads on for the Aachen dataset.
The results showed that the deviation between the
measured and predicted thermal load in terms of
MAE were 4.56 kW and 2.94 kW, respectively for
summer and winter mode. The resulting RMSE were
respectively 5.79 kW and 3.87 kW, which indicates
that the cooling energy consumption can be predicted
with lower relative error, while the absolute accuracy
in both summer and winter mode was in a similar
Spatial load granularity versus model perfor-
Table 5 summarizes the performance of the proposed
method for the ﬂoor-wise granularity case, in both
winter and summer mode.
Table 5: Floor-wise model performance on the Aachen
Floor MAE RMSE NRMSE R2
ID [kW] [kW] [-] [-]
EG 1.17 1.56 0.10 0.85
OG1 2.03 2.69 0.07 0.88
OG2 2.46 3.14 0.07 0.89
EG 1.04 1.31 0.09 0.69
OG1 1.37 1.85 0.08 0.81
OG2 1.81 2.22 0.07 0.85
Additionally, the simulated and measured trends
from the test set are represented in Figure 4. Here,
”EG”, ”OG1” and ”OG2” stand respectively for the
ﬁrst, second and third ﬂoor of the Aachen building.
It is shown that the model could represent the HVAC
on a building- and ﬂoor-wise level with similar per-
formance. The pattern behind the superposition of
several zones could be identiﬁed using an identical
modeling approach as the building-wise energy con-
sumption modeling approach.
Finally, the model’s performance for the room-wise
granularity case is presented in Table 6. Due to the
limited space, only the mean result over 73 oﬃces, as
well as the oﬃces with the highest and lowest pre-
dictive error are presented. Further results will be
released afterwards in a public library. Despite the
relatively low absolute errors (i.e. MAE and RMSE),
the R2value was negative for some rooms. According
to Equation 4, this could occur in case the mean of
the real data resulted in a better ﬁt than the estima-
tion of the model, as conﬁrmed in Figure 5.
Table 6: Room-wise model performance on the
Room MAE RMSE NRMSE R2
ID [kW] [kW] [-] [-]
max 0.57 0.80 0.23 0.44
mean 0.21 0.33 0.21 0.45
min 0.05 0.11 0.14 -2.62
max 0.72 0.96 0.27 0.16
mean 0.15 0.26 0.19 -0.14
min 0.02 0.04 0.06 -0.53
Figure 4: Floor-wise monthly course of simulated and
measured thermal loads for the Aachen dataset.
Figure 5: Monthly course of simulated and measured
thermal loads for a single Aachen oﬃce, in case of
The aim of this study was to explore the impact of the
spatial granularity on the accuracy of the data-driven
models for energy consumption prediction. The inde-
pendent round-robin study conﬁrmed that the RNN-
based modeling approach proposed by Chen et al.
(2017) is suitable for predicting the building-wise en-
ergy consumption. The results of the latter study
could be reproduced and the obtained NRMSE was
equal to 0.05, namely for 0.01 lower, when compared
to the performance reported by the original study.
This non-signiﬁcant deviation in the NMSE could be
attributed to the random initialization and updates
in the used Keras and Tensorﬂow libraries for the im-
plementation of the RNN models.
After validating the existing model, the further po-
tential for improving the model’s performance was
explored. Here, the optimization potential was ana-
lyzed for the inclusion of the longer input sequence
duration, using alternative optimizer for model train-
ing and further hyperparameter tuning. The results
showed that the accuracy could be slightly improved
by using SGD with momentum, while the inclusion of
longer input sequences did not lead to performance
improvements. The results obtained from the re-
peated hyperparameter tuning showed that the per-
formance on diﬀerent datasets could be optimized by
ﬁne tuning the hyperparameters.
The optimal neural network architecture and model-
ing approach were identical in case of both datasets.
This implies that these design decisions are dataset-
agnostic. Based on these results, it is worth to further
investigate deep learning models for generic energy
consumption predictions and to investigate which de-
sign decisions lead to dataset-agnostic model. The
obtained results could be used to formulate the ini-
tial hypothesis. Namely, an arbitrary neural network
that consist of a layer with units for sequential mod-
eling in addition to a small number of feedforward
layers (such as three layers in the scope of this study)
should provide suﬃcient learning capacity for predic-
tive energy consumption models.
In contrast to the shared optimal model design and
hyperparameters between diﬀerent datasets, the re-
sults showed that the chosen spatial granularity has
a direct impact on the predictive performance. The
predictive performance dropped signiﬁcantly in case
of oﬃce-wise HVAC energy consumption prediction,
when compared to the ﬂoor-wise or building-wise spa-
Eventually, the accuracy of the model for various pre-
dictive horizons was further investigated. The anal-
ysis was carried out for the whole Aachen dataset,
up to 12 hours ahead in hourly steps. Due to
space constraints, the results are accessible through a
public repository (TBA). The modeling performance
dropped with the increase in predictive horizon, with
the R2score dropping to 0.51 for ﬁve hours ahead en-
ergy consumption modeling. Here, the use of a longer
input sequence duration, namely from 6 hours to 1
week, could lead to better predictive performance as
already observed in Markovic et al. (2020).
The aim of this study was to explore the performance
of a RNN based model for predicting the energy con-
sumption at diﬀerent spatial granularities and for a
set of target functions such as total energy consump-
tion, HVAC cooling load, and HVAC heating load.
The novelty and the key ﬁndings may be summarized
•It could be hypothesized that narrow neural net-
works with a one hidden layer with sequential
connections and several hidden feedforward lay-
ers represents a dataset-agnostic model architec-
ture for energy consumption prediction.
•The general pattern behind explored target func-
tions such as total energy consumption, HVAC
cooling load, and HVAC heating load could be
successfully modeled using identical algorithms,
by repeating the model’s training on each target
•The HVAC loads could be predicted with an
identical performance on the building spatial
granularity and multi thermal zone level (ﬂoor-
•The predictive performance drops signiﬁcantly
at the single thermal zone (oﬃce-level) spatial
granularity, which conﬁrmed earlier ﬁndings by
Kalogirou et al. (1997).
Part of this work was funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research
Foundation) – TR 892/4-1 – and by the German Fed-
eral Ministry of Economics and Energy (BMWi) as
per resolution of the German Parliament under the
funding code 03EN1002A. We thank the EBC Insti-
tute, E.ON ERC at RWTH Aachen University for
providing the monitoring data. This paper beneﬁted
greatly from discussions with members of IEA EBC
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