# Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings

arXiv: https://arxiv.org/abs/2111.12066 · HTML: https://mlsanity.com/paper/2111.12066/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 23 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [Blending MPC & Value Function Approximation for Efficient Reinforcement Learning](https://mlsanity.com/paper/2012.05909/) (2020)
- [Model-predictive control and reinforcement learning in multi-energy system case studies](https://mlsanity.com/paper/2104.09785/) (2021)
- [Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC](https://mlsanity.com/paper/2110.15911/) (2021)
- [Data-driven Predictive Control for Unlocking Building Energy Flexibility: A Review](https://mlsanity.com/paper/2007.14866/) (2020)
- [Experimental Demonstration of Frequency Regulation by Commercial Buildings - Part I: Modeling and Hierarchical Control Design](https://mlsanity.com/paper/1605.05835/) (2016)
- [Trajectory tracking with an aggregation of domestic hot water heaters: Combining model-based and model-free control in a commercial deployment](https://mlsanity.com/paper/1805.04228/) (2018)

## Built on by (most cited first, 24 of 24)

- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Physics-informed neural networks for PDE-constrained optimization and control](https://mlsanity.com/paper/2205.03377/) (2022)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Simulating Three-dimensional Turbulence with Physics-informed Neural Networks](https://mlsanity.com/paper/2507.08972/) (2025)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [Distill2Explain: Differentiable decision trees for explainable reinforcement learning in energy application controllers](https://mlsanity.com/paper/2403.11907/) (2024)
- [The Smart Buildings Control Suite: A Diverse Open Source Benchmark to Evaluate and Scale HVAC Control Policies for Sustainability](https://mlsanity.com/paper/2410.03756/) (2024)
- [Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Models](https://mlsanity.com/paper/2212.12380/) (2022)
- [Demand response for residential building heating: Effective Monte Carlo Tree Search control based on physics-informed neural networks](https://mlsanity.com/paper/2312.03365/) (2023)
- [Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells](https://mlsanity.com/paper/2403.02289/) (2024)
- [Combining Physics-based and Data-driven Modeling for Building Energy Systems](https://mlsanity.com/paper/2411.01055/) (2024)
- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Real-World Implementation of Reinforcement Learning Based Energy Coordination for a Cluster of Households](https://mlsanity.com/paper/2310.19155/) (2023)
- [Robust Neural IDA-PBC: passivity-based stabilization under approximations](https://mlsanity.com/paper/2409.16008/) (2024)
- [Integrating Symbolic Neural Networks with Building Physics: A Study and Proposal](https://mlsanity.com/paper/2411.00800/) (2024)
- [Integrating Physics-Based and Data-Driven Approaches for Probabilistic Building Energy Modeling](https://mlsanity.com/paper/2507.17526/) (2025)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [One-shot backpropagation for multi-step prediction in physics-based system identification -- EXTENDED VERSION](https://mlsanity.com/paper/2310.20567/) (2023)
- [Opening the Black Box: Towards inherently interpretable energy data imputation models using building physics insight](https://mlsanity.com/paper/2311.16632/) (2023)
- [Generalizable Temperature Nowcasting with Physics-Constrained RNNs for Predictive Maintenance of Wind Turbine Components](https://mlsanity.com/paper/2404.04126/) (2024)
- [Partially stochastic deep learning with uncertainty quantification for model predictive heating control](https://mlsanity.com/paper/2504.03350/) (2025)
- [Input convex neural networks as surrogates in mathematical optimisation](https://mlsanity.com/paper/2608.09707/) (2026)
- [Contextual Quality-Diversity Evolutionary Reinforcement Learning for HVAC Control in Tropical Commercial Buildings](https://mlsanity.com/paper/2608.11324/) (2026)

## Abstract (arXiv)

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.