Source-linked AI summary
Physics-informed machine learning for building performance simulation-A review of a nascent field
Zixin Jiang, Xuezheng Wang, Han Li, Tianzhen Hong, Fengqi You, Ján Drgoňa, Draguna Vrabie, Bing Dong
TL;DR
Building performance simulation is valuable but difficult to scale with conventional physics-based models, while purely data-driven models can lack generalization and physical consistency. This review systematically examines physics-informed machine learning for BPS, defining its methods, applications, resources, validation issues, and selection guidance. It reports application-level performance improvements and identifies integration and real-world verification as continuing challenges.
Problem
Traditional physics-based BPS requires detailed information and calibration, while purely data-driven models can have limited generalization and physical consistency.
Method
The study systematically reviews PIML for BPS, covering its methodologies, applications, validation approaches, resources, model-selection guidance, challenges, and future directions.
Results
PIML applications reported improved prediction, control, and optimization outcomes, including lower errors, energy savings, and improved thermal comfort across reviewed studies.
Takeaways & Limitations
The review provides a structured basis for selecting PIML approaches across BPS applications while identifying adaptive methods, advanced architectures, and standardized benchmarks as development opportunities.
Takeaways & Limitations
PIML remains difficult to validate in real-world conditions because available historical measurements often omit extreme or atypical events.
Abstract
from arXiv · showhide
Building performance simulation (BPS) is critical for understanding building dynamics and behavior, analyzing performance of the built environment, optimizing energy efficiency, improving demand flexibility, and enhancing building resilience. However, conducting BPS is not trivial. Traditional BPS relies on an accurate building energy model, mostly physics-based, which depends heavily on detailed building information, expert knowledge, and case-by-case model calibrations, thereby significantly limiting their scalability. With the development of sensing technology and increased data availability, there is a growing attention and interest in data-driven BPS. However, purely data-driven models often suffer from limited generalization ability and a lack of physical consistency, resulting in poor performance in real-world applications. To address these limitations, recent studies have started to incorporate physics priors into data-driven models, a methodology called physics-informed machine learning (PIML). PIML is an emerging field with the definitions, methodologies, evaluation criteria, application scenarios, and future directions that remain open. To bridge those gaps, this study systematically reviews the state-of-art PIML for BPS, offering a comprehensive definition of PIML, and comparing it to traditional BPS approaches regarding data requirements, modeling effort, performance and computation cost. We also summarize the commonly used methodologies, validation approaches, application domains, available data sources, open-source packages and testbeds. In addition, this study provides a general guideline for selecting appropriate PIML models based on BPS applications. Finally, this study identifies key challenges and outlines future research directions, providing a solid foundation and valuable insights to advance R&D of PIML in BPS.
Nomenclature
The nomenclature table lists terms and acronyms used throughout the paper, including BPS, HVAC, CFD, IEQ, DERs, FDD, IAQ, TRV, ODE, and reduced resistor-capacitor models.
- Table 1 provides the paper’s nomenclature and acronym definitions.
- BPS denotes Building Performance Simulation, while HVAC denotes Heating, Ventilation, and Air Conditioning.
- CFD, IEQ, and DERs denote Computational Fluid Dynamics, Indoor Environment Quality, and Distributed Energy Resources, respectively.
- FDD, IAQ, TRV, and ODE denote Fault Detection and Diagnostics, Indoor Air Quality, Temperature Response Violation, and Ordinary Differential Equation.
- The paper also defines the Reduced Resistors and Capacitors Model.
1. Introduction
The introduction positions BPS as important for energy and environmental performance but difficult to scale because physics-based and purely data-driven approaches have complementary limitations. It presents PIML as an emerging integration strategy and frames this review as a systematic account of its methods, applications, resources, and research directions.
- Buildings account for approximately 34% of global energy use and 37% of CO₂ emissions, making building energy-efficiency optimization important.
- BPS uses mathematical models to simulate energy flows, airflows, lighting, thermal comfort, and other IEQ metrics for design, operation, retrofitting, and planning.
- Physics-based BPS models rely on detailed metadata and governing equations, while their computational burden can become prohibitive as model complexity increases.
- Data-driven models avoid requiring prior physical characteristics but generally depend on collected or simulated data and are less relevant at the building-design stage.
- PIML integrates physics-based and data-driven modeling to target scalable, accurate, and physically consistent BPS applications.
- This review broadens prior work by covering PIML definitions, methodologies, applications, resources, challenges, selection guidance, and future directions across BPS.
2.1. Definition of physics-informed machine learning
PIML is defined as a hybrid framework that embeds physical laws and expert knowledge into machine-learning processes. This integration is intended to improve generalization, physical consistency, and data efficiency.
- PIML integrates fundamental physical laws with machine-learning techniques in a hybrid modeling framework.
- Physics knowledge can enter model architectures, loss functions, parameters, or training algorithms through equations or domain-specific knowledge.
- The framework is described as improving predictions on unseen scenarios, physical consistency, and reducing data requirements.
2.2. Key approaches to incorporate physics into machine learning
The review organizes BPS PIML methods around four integration types—physics-informed datasets, loss functions, model structures, and hard constraints—and discusses how explicit equations, expert knowledge, and surrogate models differ in rigor and flexibility.
- BPS PIML approaches are categorized as physics-informed datasets, loss functions, model structures, and hard constraints.
- Physics-informed data set: Physics-informed datasets use data designed or generated to reflect physical principles, but data alone does not qualify as PIML without physics priors contributing to predictions.
- Physics-informed data set: Ensemble learning combines a physics-driven component with a data-driven residual model, but its sequential dependence on calibrated physics-based models can limit scalability.
- Physics-informed loss functions: Physics-informed loss functions add physics constraints as penalty terms alongside standard prediction losses during training.
- Physics-informed loss functions: Governing-equation losses, including PINNs, encode differential equations and boundary or initial conditions, whereas knowledge-guided losses use expert-derived physical priors when equations are unavailable.
- Physics-informed loss functions: Surrogate physics-based losses use reduced physical models to generate pseudo-labels for unobservable states and guide learning.
- Physics-informed loss functions: Governing-equation losses generally provide the strongest physical consistency, while knowledge-guided and surrogate losses offer greater flexibility under incomplete or uncertain physical information.
2.3. Model verification
Model verification must assess physical consistency in addition to predictive accuracy, especially because unconstrained models can respond incorrectly to control inputs and unseen conditions. The review summarizes sanity checks, TRV, MMD, gradient, and eigenvalue evaluations for this purpose.
- Motivation: Unconstrained LSTM models may fit accurately yet fail to represent heating and cooling effects, particularly under unseen HVAC conditions.Limited training-data coverage can produce incorrect input-output relationships and controller failures.
- Evaluation rationale: Accuracy metrics such as MAE, MAPE, MSE, and RMSE do not establish whether a model responds physically to control inputs.The review therefore treats physical-consistency evaluation as a necessary complement to conventional regression metrics.
- Model sanity check: Sanity checks reset HVAC inputs while holding other features fixed, then assess the response sign, speed, and amplitude against expected behavior.The reset can begin at a selected timestep, such as the third timestep, and use maximum or minimum capacity.
- Model sanity check: TRV quantifies consistency violations from predicted responses under modified inputs, with zero violations expected for a physically consistent model.The metric uses predictions from the original input and modified sanity-check inputs.
- Complementary metrics: TRV verifies only the sign of system gain, so MMD compares response distributions to measured data when magnitude and response speed also matter.Smaller MMD indicates closer alignment between model and real-system responses.
- Additional evaluations: Gradient evaluation checks input-output sensitivities, while eigenvalue evaluation checks feasibility and stability of the modeled dynamic system.For thermal prediction, expected gradients can reflect nonnegative effects and temporal decay; eigenvalue tests use the Hautus stabilizability condition.
3. Physics-informed machine learning in building performance simulation: applications, resources, and comparisons
PIML applications in BPS span IEQ assessment, control and optimization, energy prediction, fault diagnostics, airflow simulation, and distributed-energy integration. Reported studies combine physical constraints or governing equations with learned models to improve accuracy, efficiency, control outcomes, or data use, while some remain limited by simplified settings or computational cost.
- IEQ assessment: IEQ applications cover temperature, humidity, CO₂, lighting, sound, and thermal-comfort modeling, with temperature prediction the most common focus.The review also identifies control, airflow, energy prediction, and BTM DER integration as major application areas.
- IEQ assessment: 0.59 K MSE was achieved for 30-day multizone temperature prediction using only 10 days of training data, versus 1.07 K for the best linear model.Other studies reported lower errors than RC, LSTM, PINN, or conventional baselines across single-zone and multizone tasks.
- IEQ assessment: 10 dB lower RMSE than state-of-the-art methods was achieved for room impulse-response reconstruction with sparse observations, while other acoustic models improved efficiency or reduced dense sensor dependence.Reported acoustic applications include time-varying wave simulation, reverberant-room reconstruction, and three-dimensional studio-field prediction, with simplified or controlled settings limiting broader validation.
- Control and system optimization: 27% lower peak demand and 22% lower energy consumption were achieved by PCNN-enabled MPC relative to baseline control, alongside higher self-sufficiency and PV self-consumption.Other PIML controllers reported energy, comfort, cooling-load, and cost improvements, although nonlinear optimization could impose high computation cost.
- Energy prediction and analysis: 95.37% detection and diagnosis rates with a 0.73% error rate were reported for AHU fault detection, while physics-guided prognosis improved accuracy and data efficiency over GP, SVM, and RNN baselines.Load-prediction studies reported R² values of 0.79–0.94 and MAE values of 0.11–0.73 kW under varied conditions.
- Airflow simulation: 70% lower error rates and 42% shorter computing time were reported for PINN airflow reconstruction than traditional artificial neural networks in small two-dimensional environments.Urban-scale models combine sparse measurements or CFD-generated data with governing equations, while simplified geometries and boundary assumptions constrain applicability.
3.2. Available resources to support research and development in physics-informed machine learning
The review identifies datasets, physics-informed tools, and open-source testbeds as resources for developing and benchmarking PIML in BPS. These resources support reproducibility and evaluation, but performance across climates, buildings, weather conditions, and HVAC systems remains an open question.
- Datasets: Open datasets include multiyear apartment, office-building, and residential smart-thermostat measurements covering building operations, weather, and energy-related variables.Examples include more than three years from the NEST apartment, a three-year Berkeley office timeseries with over 300 sensors and meters, and 2017 data from 1,000 homes.
- Evaluation scope: Performance across varying climates, weather patterns, building types, and HVAC systems remains an open question for the emerging PIML field.The review motivates open-source datasets and benchmarking resources to examine these conditions.
- Packages: Physics-informed neural-network solvers provide reusable tools for forward and inverse problems involving PDE-based building applications such as heat transfer, airflow, and lighting.The cited tools primarily incorporate governing equations into training loss functions.
- Packages: Open-sourced building-dynamics models support fast prediction of space temperature and humidity from operational data and advanced building-energy control applications.These models use customized architectures or constrained parameters and often include documentation and example scripts.
- Testbeds: BCVTB enables co-simulation among tools including EnergyPlus, Modelica, Radiance, and MATLAB/Simulink, while BOPTEST provides another testbed for benchmarking PIML models.The review presents these testbeds as resources for evaluation and benchmarking.
3.3. Comparison between physics-informed machine learning and traditional BPS approach
PIML combines physics-based and data-driven approaches to improve generalization and physical consistency, while introducing trade-offs in uncertainty, accuracy, and computational cost.
- Data requirements and modeling effort: Physics-based models require detailed metadata and substantial development effort, whereas data-driven models depend heavily on comprehensive, high-quality datasets.Physics-based workflows include geometry, envelope, system schedules, meshing, and boundary conditions.
- Model performance: Data-driven models can achieve high accuracy under normal conditions but may generalize poorly and violate physical consistency under unseen scenarios.Their predictive uncertainty depends largely on training-data quality and coverage.
- Model performance: PIML embeds physical knowledge into data-driven models, narrowing the solution space to improve generalization and physical consistency while reducing epistemic uncertainty.The review cites a disruptive power-outage evaluation in which a PIML model captured temperature behavior correctly.
- Model performance: PIML cannot fully address aleatory uncertainty, and its physical constraints may reduce accuracy on standard datasets relative to purely data-driven models.PINNs have also not consistently outperformed traditional numerical solvers, especially for nonhomogeneous problems and abrupt material interfaces.
- Computation cost: Physics-based computation can grow exponentially with model complexity, while data-driven models require training but offer rapid inference after training.Training cost depends on model structure, dataset size, batch size, and training epochs.
4. Discussion
The review identifies challenges in selecting and implementing PIML methods, balancing physical fidelity with data-driven flexibility, and validating models for real-world BPS applications.
- 4.1. Model selection: Governing equation-based losses offer high physical fidelity for fine-grained simulations, while knowledge-guided losses rely more heavily on expert knowledge.Governing-equation losses require well-defined equations and boundary conditions; knowledge-guided losses can improve efficiency, accuracy, and generalizability when prior knowledge exists.
- 4.2.1. Trade-offs: Physics-informed models increase development complexity through expert-driven architecture design, multiple regularization losses, weight tuning, and feature-scaling requirements.BPS quantities can differ by orders of magnitude, requiring reformulated equations, unit conversion, and regularization-weight tuning.
- 4.2.1. Trade-offs: Physics constraints can limit model expressiveness and predictive accuracy when simplified or approximate physical equations restrict complex nonlinear relationships.The resulting trade-off is between physical interpretability and the flexibility of purely data-driven models.
- 4.2.1. Trade-offs: Higher model complexity can increase computational cost and hinder real-time control, whereas simplified models may sacrifice accuracy to enable convex, control-friendly optimization.Some complex models require particle swarm optimization or dynamic programming, while simplified models can be reformulated as convex optimization problems.
- 4.2.2. Integrating physics priors: Efficient physics integration remains an open question involving data requirements, training and utilization costs, and targeted model structures and priors.Physics-informed datasets may come from experiments or simulations, but standardized benchmarks are lacking and simulation-generated data can inherit scalability problems.
- 4.2.3. Evaluation and verification: Current evaluations emphasize MAE and MSE more than physical behavior, while historical test data may not cover the full range of real-world operating scenarios.The review calls for stronger assessment of response dynamics and verification beyond typical historical conditions.
- 4.3. Future directions: Future directions include adaptive physics-data integration, bidirectional knowledge embedding and discovery, hybrid spatial-temporal architectures, efficient optimization, and standardized multi-domain frameworks.The review also identifies emerging applications including renewable integration, smart-grid optimization, indoor farming, and urban-scale environmental simulation.
5. Conclusions
The review presents PIML as a bridge between physics-based and data-driven BPS, summarizes its applications and barriers, and identifies adaptive methods, advanced architectures, and benchmarks as development opportunities.
- 5. Conclusions: PIML integrates physical principles into machine learning to improve predictive accuracy, generalization ability, and physical consistency in BPS.The review frames this integration as addressing limitations of both traditional physics-based and purely data-driven approaches.
- 5. Conclusions: The review defines PIML, summarizes methodologies and applications, and identifies barriers involving physics-data balance, efficient prior integration, and real-world verification.Covered applications include IEQ assessment, control and system optimization, and airflow simulation.
- 5. Conclusions: Future opportunities include adaptive methodologies, advanced neural architectures, standardized benchmarks, and applications in smart control, urban energy planning, and climate resilience.The review states that realizing this potential requires continued research, methodological refinement, and broader application.
CRediT authorship contribution statement
The authors contributed across writing, methodology, investigation, conceptualization, visualization, software, and resources.
- CRediT authorship contribution statement: The contribution statement assigns authorship across writing, methodology, investigation, conceptualization, visualization, software, and resources.Multiple authors contributed to writing, methodology, investigation, and conceptualization.
Declaration of competing interest
The authors report no known competing financial interests or personal relationships affecting the work. One author’s editorial role did not involve the review or publication decision.
- The authors declare no known competing financial interests or personal relationships that could have influenced the reported work.
- An author’s editorial role was separated from the article’s editorial review and publication decision.