Hybrid Physics-Data Modelling of Building Thermal Dynamics

The EU-funded Horizon Europe project ENTRANCE transforms buildings into active energy system nodes through digitalization and AI-driven HVAC control. This work blends physics-based equations with neural networks to develop a largely interpretable thermal model of one of ENTRANCE’s pilot buildings. Building dynamics is learnt from typical monitoring data, enabling a plug-and-play predictive control tool through physics-informed residual forecasting.

Key words: building energy model, greybox, residual approach, neural network, Horizon Europe, HVAC systems, interoperability, smart buildings

Why entrance

The building sector in Europe is responsible for around 40% of the total energy consumption and 36% of greenhouse gas emissions. In the ongoing energy transition, buildings play a crucial role because they can integrate advanced control strategies and smart energy management systems more easily than other sectors. Improving energy efficiency and flexibility in a cost-effective way, while enhancing users’ comfort, productivity, and health, opens the door to a faster integration of on-site and nearby renewable energy sources (RES), demand electrification, and reduced energy dependency.

Achieving these goals, however, requires buildings to become more interoperable with energy carriers and services. This is the challenge that gave rise to ENTRANCE, an EU-funded Horizon Europe Innovation Action under the Climate, Energy and Mobility cluster.

What entrance is

At its heart, the initiative is built on four interconnected principles:

·         integrating technology,

·         digitalization,

·         users’ engagement, and

·         performance-driven economics.

These principles guide the implementation of eleven innovative solutions, which will be demonstrated in six pilot sites across Europe. Rather than treating buildings as passive energy consumers, the project envisions them as active nodes in the energy system, capable of interacting with the grid, responding to changing conditions, and supporting decarbonization.

ENTRANCE Pilot locations

To reach this vision, the consortium has set seven strategic objectives, including:

·         Develop flexibility enhancement and building-to-grid integration processes and products,

·         Develop services for building participation in the energy markets,

·         Empower users and improve experience of energy service and contract management,

·         Contribute to operational energy performance, smart readiness, and flexibility

·         Demonstrate the applicability and effectiveness of the project results in operational environments

·         Develop performance-based economic evaluation

·         Foster the EU-wide uptake and replication of the project results

These ambitions are backed by clear impact targets:

·         20% increase in building-to-grid integration efficiency,

·         30% reduction in overall energy use,

·         improved grid stability and resilience through real-time communication between buildings and energy networks, and

·         30% improvement in smart readiness.

The technical structure of the project lies in the combination of smart energy systems, digital platforms, and AI-driven control strategies. Advanced IoT infrastructures collect high-resolution performance data, while machine learning and big data analytics enable predictive and adaptive control of HVAC and other energy systems. This allows buildings to anticipate and respond to occupancy patterns, weather changes, and grid signals, ensuring both comfort and energy savings. In this way, the project positions artificial intelligence as a practical enabler of flexible, low-carbon building operation.

Who entrance is

This effort is driven by a multidisciplinary European consortium of research institutions, industry innovators, and energy experts. Coordinated by the Norwegian University of Science and Technology (NTNU), the project brings together 11 partners from across Europe.

Academic and research excellence comes from Aalborg University (Denmark), Politecnico di Torino (Italy), Lublin University of Technology (Poland), and Tallinn University of Technology (Estonia), who provide expertise in energy systems, digitalization, and smart control. Key industrial actors, CIT Renergy (Sweden), ReMoni (Denmark), Norconsult (Norway), EURIX (Italy), and PORT PC (Poland), ensure that the technologies developed are not only innovative but also applicable at scale. The European HVAC federation REHVA (Belgium) acts as a bridge between research and industry, supporting communication, dissemination, and market uptake.

Bringing these diverse strengths together reflects the project’s core philosophy: combining technical excellence, user engagement, and economic insight to accelerate the transition toward a smarter, cleaner, and more resilient built environment.

Background

ENTRANCE’s task T4.1 focuses on data-driven dynamic models for enhancing energy flexibility. Several studies have explored how to draw on HVAC flexibility using advanced control strategies, such as model predictive control (MPC) [1]. However, these strategies rely heavily on accurate physics-based models that can predict how buildings respond to weather, solar irradiance, internal heat gains, and control input. Developing these models is challenging. Traditional physics-based models often oversimplify real dynamics and require extensive data about the building envelope, HVAC systems, and occupancy. This data is often unavailable or hard to obtain. Conversely, data-driven models tap into measured data to infer thermal dynamics with less effort; however, they often lack physical interpretability.

This work presents a hybrid framework, which aims to develop a simple, physics-informed, interpretable data-driven model of the thermal dynamics of one of ENTRANCE’s pilot buildings. Ideally, the model should be deployable within hours and not rely on lengthy, time-consuming building energy simulations. Moreover, this work aims to assess whether the building’s thermal dynamics can be modeled using available monitoring data. This work is also linked to ENTRANCE’s task T5.1, which defines how ENTRANCE’s solutions are implemented and includes the monitoring and metering plan.

Method

A residual approach [2] is adopted, which combines a lumped-parameter resistance-capacitance (RC) model with a neural network correction. The approach preserves thermodynamic interpretability and increases accuracy. The method leverages monitoring data from pilot IT1; that is, from the Energy Center, a four-story building in Turin, Italy. IT1 houses offices, meeting rooms, and an auditorium. IT1 is heated by district heating and by a multi-purpose air-water heat pump using groundwater as a thermal source. In winter, IT1 is mainly heated by district heating. The first-order RC model represents IT1's thermal dynamics through Eq. (1).

Eq. (1) considers indoor air as thermal node. Ti and Tout are the indoor and outdoor air temperature, respectively. Ci is the thermal capacitance of indoor air. ΦDH is the power supplied by the district heating network. Φsun is the global horizontal irradiance. bIG models baseline internal gains from occupancy and equipment. The aforesaid neural network models the schedule-dependent internal gains because simplified assumptions about their behavior with time increase the error of the RC model. Term c (Ti − Tout) models the heat loss through the envelope. Term ∑nj dj (Ti − Tout) models ventilation losses from the air handling units (AHUs) serving the auditorium and offices in the NE and NW wing. nj is the speed modulation of the return fan of a given AHU.

Eq. (1) is discretized using the backward Euler method. According to a greybox-modelling approach, parameters Ci, a, bIG, c and dj are identified through bounded constrained optimization. The optimization uses monitoring data with 15-minute resolution from the 2024-2025 heating season (13452 samples). The dataset features indoor and outdoor air temperatures, heat supplied by the district heating network, and speed modulation signals from AHUs. Hourly solar radiation data is obtained from the POWER Project's Hourly API 2.8.0 version on 2025/09/29.

64 indoor temperature time series are provided. The series with the most median values across timesteps is selected as Ti. This choice guards against outliers and helps track temperature transients in a representative room.

To account for IT1’s thermal inertia, after simplifying the ARIMAX model in [3], the district heating power is modelled as a Finite Impulse Response (FIR) filter; that is, as a weighted sum of current and past heating powers over a 4-hour window. The 4-hour window helps minimize the residual. Each weight includes a fixed term and a Monday-specific term to model the longer warmup time when IT1 is cold after the weekend. The FIR weights are constrained to sum to 1.

Method ‘trust-constr’ from library SciPy [4] is used to perform the optimization and to find Ci, a, bIG, c, djand FIR weights. The mean squared difference between LHS and RHS of Eq. (1) is set as the objective function.

Despite capturing the overall dynamics, the optimized RC model yields systematic residuals, mainly during morning warm-up and evening cooldown times. A feedforward neural network (FFNN) built in PyTorch [5] mitigates this issue by learning and forecasting time-varying residuals. Since the residual exhibits daily and weekly patterns arising from unmodeled dynamics, time features – namely, minutes since midnight and day of week - are fed to the FFNN to estimate the residual. The FFNN is trained using the root mean squared error (RMSE) between true and forecast residuals as a loss function. A 70-15-15 train-test-validation split is performed. Library Optuna [6] helps to optimize hyperparameters; namely, number of layers and neurons per layer, dropout rate, batch size, learning rate. The best model is trained using the Adam optimizer.

Results

Figure 1 shows selected terms from Eq. (1)and the residual (i.e., the difference between RHS and LHS) between January 22 and 27, 2025. This time range is part of the test dataset. The residual appears to be high when the first-order RC model fails to model heat storage in walls, tanks and pipes, when measurement errors occur or when schedule-dependent internal gains are significant. Parameters a and bIG are found to be negligible. The mean absolute error (MAE) is 20.9 kW on the test dataset. For comparison, the average ΦDHis 62.8 kW.

Figure 2 helps to compare the actual residual with the residual forecast by the FFNN. The hybrid model improves the physics-only approach: the FFNN can learn the overall trend and periodic patterns. The MAE on the test dataset decreases from 20.9 kW to 14.3 kW. This is an early-stage result from ongoing work, and given that only two features were fed to the FFNN, the MAE reducion is deemed acceptable.

Figure 1. Terms in Eq. (1) and actual residual.

Figure 2. Actual and forecast residual.

Conclusions

By blending optimization-based parameter identification with a neural forecaster, the approach outlined here can reconcile theoretical modeling and operational reality. The outcome is a model that is largely interpretable, easy to set up and take up: the method relies on standard monitoring data, such as temperatures, heating input, and fan signals, so it is suitable for buildings with basic energy management systems. The 15-minute resolution is widely used in HVAC control.

Future work will target 3 areas to increase accuracy and reliability: 1) Eq. (1) will account for energy storage in walls, tanks, and pipes, as well as for measurement errors and thermal zones. The backward Euler discretization requires knowledge of exogenous variables at the next timestep, so these are likely to be replaced with predictions from weather forecast APIs (e.g., for Tout) or from forecasting models (e.g., for ΦDH). 2) The FFNN will take in more input features and be trained with a physics-informed loss function, similar to those used in physics-informed neural networks (PINNs). 3) Fast operational patterns will be modeled to enable predictive control strategies that forecast building response and optimize energy management in real time.

References

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[2]     L. V. Krannichfeldt, K. Orehounig, and O. Fink, “Combining Physics-based and Data-driven Modeling for Building Energy Systems,” Appl. Energy, vol. 391, p. 125853, Aug. 2025, doi: 10.1016/j.apenergy.2025.125853.

[3]     Y. Zhang, X. Tian, Y. Zhao, C. Zhang, Y. Zhao, and J. Lu, “A prior-knowledge-based time series model for heat demand prediction of district heating systems,” Appl. Therm. Eng., vol. 252, p. 123696, Sept. 2024, doi: 10.1016/j.applthermaleng.2024.123696.

[4]     P. Virtanen et al., “SciPy 1.0: fundamental algorithms for scientific computing in Python,” Nat. Methods, vol. 17, no. 3, pp. 261–272, Mar. 2020, doi: 10.1038/s41592-019-0686-2.

[5]     J. Ansel et al., “PyTorch 2: Faster Machine Learning Through Dynamic Python Bytecode Transformation and Graph Compilation,” in Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2, La Jolla CA USA: ACM, Apr. 2024, pp. 929–947. doi: 10.1145/3620665.3640366.

[6]     T. Akiba, S. Sano, T. Yanase, T. Ohta, and M. Koyama, “Optuna: A Next-generation Hyperparameter Optimization Framework,” July 25, 2019, arXiv: arXiv:1907.10902. doi: 10.48550/arXiv.1907.10902.