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Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings

Gargya Gokhale, Bert Claessens, Chris Develder

arXiv:2111.12066v2eess.SPcs.LGeess.SY

TL;DR

Building thermal control needs models that are accurate and interpretable without requiring extensive data. This paper develops physics-informed neural-network architectures that encode building physics, and reports improved data efficiency, longer-horizon prediction, and low room-temperature prediction error.

  • Problem

    Building control requires accurate models, while physics-based models are difficult to obtain and conventional data-driven models can require large datasets and lack interpretability.

  • Method

    The paper proposes two physics-informed neural-network architectures that incorporate building parameters and underlying thermal physics during training.

  • Results

    The architectures require less training data, perform better than conventional neural networks at longer prediction horizons, and achieve room-temperature prediction error below 0.25°C.

  • Takeaways & Limitations

    Physics-informed neural networks can model room temperature and building thermal-mass hidden states for control-oriented building applications.

  • Takeaways & Limitations

    Accurate household modeling is constrained by difficult hidden-state and exogenous-variable measurements and by building parameters that change over time.

Abstract

from arXiv · show

This paper presents a data-driven modeling approach for developing control-oriented thermal models of buildings. These models are developed with the objective of reducing energy consumption costs while controlling the indoor temperature of the building within required comfort limits. To combine the interpretability of white/gray box physics models and the expressive power of neural networks, we propose a physics informed neural network approach for this modeling task. Along with measured data and building parameters, we encode the neural networks with the underlying physics that governs the thermal behavior of these buildings. Thus, realizing a model that is guided by physics, aids in modeling the temporal evolution of room temperature and power consumption as well as the hidden state, i.e., the temperature of building thermal mass for subsequent time steps. The main research contributions of this work are: (1) we propose two variants of physics informed neural network architectures for the task of control-oriented thermal modeling of buildings, (2) we show that training these architectures is data-efficient, requiring less training data compared to conventional, non-physics informed neural networks, and (3) we show that these architectures achieve more accurate predictions than conventional neural networks for longer prediction horizons. We test the prediction performance of the proposed architectures using simulated and real-word data to demonstrate (2) and (3) and show that the proposed physics informed neural network architectures can be used for this control-oriented modeling problem.

1. Introduction

Building control needs accurate models, but physics-based models are costly and data-driven models can require extensive data while lacking interpretability. The paper proposes physics-informed neural-network architectures that incorporate building physics to improve control-oriented thermal modeling.

  • Motivation: Buildings are central to energy efficiency and flexibility as renewable generation increases and building energy consumption remains substantial.Buildings accounted for 40% of worldwide primary energy consumption and around 55% of EU electricity consumption as of 2016.
  • Modeling challenge: Model fidelity is crucial for model-predictive control, but obtaining accurate building models is difficult and computationally intensive.Physics models can be limited by high computational complexity, while inaccurate models undermine control performance.
  • Modeling challenge: Data-driven models avoid some physics-modeling challenges but commonly require large training datasets and provide limited interpretability.The paper identifies these as key challenges of conventional data-driven techniques such as neural networks.
  • Approach: The paper proposes physics-informed neural networks that explicitly provide underlying system physics to a deep neural network during training.The approach aims to combine self-learning, physics-guided models with model-based reinforcement learning for interpretable control agents.
  • Contributions: Two new physics-informed neural-network variants are proposed for control-oriented thermal modeling and validated using simulated and real-world data.The real-world experiments use cold-storage data to evaluate longer-horizon prediction performance and training-data efficiency.
  • Contributions: The proposed architectures require less training data and perform better than conventional neural networks for longer prediction horizons.The paper also reports that the specific architecture incorporates basic constraints based on a simple RC model and demonstrates practical feasibility with real-world data.

2. Related Work

Prior building-control work includes model-based and data-driven approaches, each with practical limitations. This paper instead learns a low-dimensional latent dynamics model with physics-informed neural networks for later use in model-based reinforcement learning.

  • Building control and modeling: Model-predictive control can produce cost savings and interpretable decisions, but it depends on accurate physical models and can be computationally expensive.Prior work reported operating-cost reductions of about 20% compared with rule-based control, while modeling and investment costs limit wider adoption.
  • Building control and modeling: Reinforcement-learning controllers reduce reliance on explicit physical models but require substantial data and exploration, including potentially unsafe interactions.Examples in prior work used one year of data or two months of temperature data equivalent to 3000 simulated trajectories.
  • Paper positioning: The paper learns a low-dimensional latent-space dynamics model for model-based reinforcement learning rather than directly using a system model.This contrasts with earlier control-oriented modeling work focused on convex, linear or bilinear, time-invariant models compatible with MPC solvers.
  • Physics-informed neural networks: Physics-informed neural networks encode prior system knowledge explicitly in the network architecture or training process.Related work applies this idea to difficult physics problems and to building thermal modeling, including physics-informed ARMAX and neural architectures.
  • Physics-informed neural networks: Earlier building applications reported improved training sample efficiency or longer-horizon prediction performance when prior physics knowledge was incorporated.The reviewed approaches include a physics-informed ARMAX model, a parallel physics-informed and black-box architecture, and a structured recurrent neural dynamics model.

3. Mathematical Modeling

The paper formulates building thermal control as a partially observable, discrete-time state-transition problem and trains physics-informed neural networks to predict future observable states and latent dynamics. Two architectures incorporate a physics-based constraint while handling hidden thermal states through learned representations.

  • Problem Formulation: The thermal system is modeled as a discrete-time Markov Decision Process in which a network predicts the next state from the current state, action, and exogenous information.The case study uses one action every 30 minutes and predicts subsequent room temperature and heating power.
  • Problem Formulation: Because building thermal systems are partially observable, past room-temperature measurements provide engineered features for compensating for unmeasured parameters such as thermal mass.The state combines observable components with a feature-engineered component.
  • Physics-Informed Formulation: The physics-informed formulation combines data regression with a physics-based constraint relating observable states, actions, exogenous factors, hidden states, and system parameters.For real-world noise and exogenous effects, the strict physical equality is replaced by a least-squares physics loss weighted by λ.
  • Physics-Informed Neural Network Architectures: One proposed architecture uses an encoder to compress engineered state features into a latent representation, then a dynamics module predicts the next observable state from that representation and other inputs.The latent representation is explicitly used by the dynamics module, ensuring it contains information about system dynamics.
  • Physics-Informed Neural Network Architectures: A second fully connected architecture predicts the next observable state and latent representation simultaneously with shared parameters, while physics guides the latent representation as a regularizer.The paper notes that this latent representation may not otherwise contain sufficient information about system dynamics.

4. Experimental Setup

The experiments evaluate physics-informed neural-network architectures for control-oriented thermal modeling using a simplified 2R2C building model, simulated data, and real-world cold-storage data. The setup tests hidden-state estimation, prediction inputs and outputs, architecture configurations, and the effect of available history.

  • Thermal model: The study models a single heated room with a grey-box 2R2C state-space formulation containing observable room temperature and hidden thermal-mass temperature.The model also includes outside temperature, solar irradiance, internal heat gains, and building heat-transfer parameters.
  • Thermal model: A backup controller keeps room temperature within predefined comfort limits, so actual power consumption can differ from demanded power.The controller applies zero, requested, or maximum power depending on whether room temperature exceeds or falls below comfort bounds.
  • Neural-network inputs and outputs: The continuous state-space model is discretized at one action every 30 minutes, with networks predicting subsequent room temperature and power consumption.Past observable states and actions are supplied because the building model is partially observable.
  • Neural-network inputs and outputs: The networks use observable states, actions, time of day, and outside air temperature to predict room temperature, power consumption, and building thermal-mass temperature.The hidden-state output is computed through the physics module and is guided toward physically relevant values by the loss functions.
  • Physics-informed configuration: Building-specific physics parameters are initialized from EPC values and tuned during training to accommodate approximate initial knowledge and natural variation.The chosen prior model is a 2R2C formulation, although other prior models could be used.
  • Data scenarios and configurations: Experiments compare simulated single-household data with real-world cold-storage data and vary sequence depth, which controls how much past information reaches the model.The simulated case uses a one-minute discretization and random actions, whereas the cold-storage case includes active control and indirectly observed exogenous effects.

5. Results and Discussions

Experiments on simulated and real-world building data evaluated the proposed physics-informed architectures across hidden-state estimation, training-data size, and prediction horizon. They generally maintained accurate thermal predictions, with stronger advantages over conventional MLPs when data were limited or horizons were longer.

  • 5.1. Architecture Validation: Both physics-informed architectures closely tracked simulated room temperature and action values while estimating the hidden thermal-mass state.The hidden-state estimates followed the actual values, supporting their use for control-oriented thermal modeling.
  • 5.1. Architecture Validation: 60−70% better hidden-state prediction was achieved by the physics-informed architectures than by conventional MLPs, whose hidden-state estimates lacked target values.The physics-informed models had hidden-state absolute errors below 0.5°C.
  • 5.2. Performance vs. Training Data Size: Both architectures accurately predicted room temperature and power consumption over five real-world test days while producing plausible hidden-state estimates.These results were reported for cold-storage-unit data.
  • 5.2. Performance vs. Training Data Size: At 12-hour horizons and 15−45 training days, physics-informed models achieved MAE at least 15% lower than MLP.For training sizes above 90 days, performance became similar across the three architectures; at shorter horizons, conventional MLP sometimes performed better.
  • 5.3. Performance vs. Prediction Horizon Size: With low training data, conventional MLP error approached 1°C at 24 hours, while physics-informed models remained around 0.75°C with ±0.3°C standard deviation.At 120 training days, mean errors were similar, but physics-informed models had narrower error distributions.
  • 5.3. Performance vs. Prediction Horizon Size: Introducing prior physics knowledge produced more sample-efficient training and models suitable for evaluating longer control trajectories.The authors connect this stability to tree searches in control applications.

6. Conclusion

The study concludes that physics-informed neural networks accurately predict building room temperature and are better suited to limited-data and long-horizon thermal modeling. The reported room-temperature prediction error was below 0.25°C.

  • Less than 0.25°C prediction error was obtained for room-temperature modeling with both physics-informed architectures.
  • Physics-informed neural networks performed better when training data were limited and prediction horizons were longer.

Future Work

Future work targets both control development and improvements to the PhysNet and PhysReg MLP architectures.

  • Future work will use the learned architectures in model-based reinforcement learning for simultaneous building-model and control-policy learning.The planned agent would also schedule upcoming hours while retaining interpretable decision making and human supervisory control.
  • Future architectural improvements include direct multi-step forecasting, recurrent networks, clustering, and transfer learning for scalable deployment.

Funding

The work was supported by European Union Horizon 2020 research and innovation projects.

  • Funding came from the Horizon 2020 projects BRIGHT, RENergetic, and BIGG.The listed grant agreement numbers are 957816, 957845, and 957047, respectively.

Appendix A. Hyperparameters for Physics Informed Neural Networks

The appendix documents the hyperparameters and tuning procedure for the two proposed physics-informed neural network architectures. Both architectures used a shared training setup, while hyperparameters were selected through validation-based grid search.

  • Both architectures were trained with batch size 2048 for 75 epochs across 20 random seeds.The models used the same hyperparameters while varying seeds from 1 to 20.
  • The appendix reports hyperparameters for the PhysReg MLP and PhysNet architectures.These are presented in Tables A.3 and A.4.
  • Hyperparameters were selected by grid search using validation-set mean absolute error.Neural-network hyperparameters were tuned first with λ set to 0, followed by tuning the physics-informed parameters.

Appendix B. Training Time and Hardware Configuration

The appendix describes repeated neural-network training for prediction aggregation and reports the associated training-time and hardware configuration. Twenty independently initialized instances were trained, and their mean prediction was used.

  • Twenty neural-network instances with different random initializations were trained for the Section 5.1 results.All instances used the same hyperparameters.
  • The predictions from the 20 trained instances were averaged before use.The mean of their predictions was used for the reported results.
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