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\title{Bridging the Simulation-to-Reality Gap: A Hybrid Data-Driven Framework for AI-based Prediction of Building Energy Retrofit Performance}
\author{Zichen Liang \and Collaborators}
\date{}

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\begin{abstract}
\textbf{Motivation.} Predicting the realized performance of building energy retrofits remains hard due to a persistent simulation-to-reality (Sim2Real) gap caused by construction and operation uncertainties, sensor biases, and occupant behavior.
\textbf{Objective.} We present a hybrid, data-driven framework that (i) trains on large, standardized simulation corpora and (ii) calibrates and evaluates on curated real-world monitoring datasets to quantify and reduce Sim2Real error.
\textbf{Method.} We design a \emph{Train-on-Simulation, Test-on-Real} protocol with domain shift diagnostics, representation alignment, and error decomposition. Tabular learners (XGBoost/LightGBM) are paired with physics-informed features and post-hoc conformal uncertainty quantification. 
\textbf{Results.} In in-domain tests, the proposed models achieve state-of-the-art accuracy on held-out simulated cases; when tested on real retrofits with measurement verification (ASHRAE~14/IPMVP), Sim2Real error is reduced by combining (a) physics proxies, (b) domain-adaptive reweighting, and (c) lightweight field calibration.
\textbf{Contributions.} (1) A transparent Sim2Real evaluation protocol for retrofit prediction, (2) a hybrid methodology that is robust under data scarcity, and (3) reproducible assets (code, datasets, and experiment cards).
\end{abstract}

\section{Introduction}
Energy retrofits are central to decarbonizing the building stock, yet stakeholders still lack reliable ex-ante predictions of realized savings and indoor environmental quality (IEQ) improvements. Traditional physics-based simulations (e.g., EnergyPlus/TRNSYS) provide detailed process understanding but are labor intensive and sensitive to input assumptions; purely data-driven models offer speed but overfit to data regimes that rarely match deployment contexts. This misalignment produces a persistent Sim2Real gap that undermines trust and investment decisions. 
We investigate: \emph{To what extent can models trained on large simulated retrofit corpora generalize to real projects, and which hybrid strategies measurably narrow this gap?}
Our contributions are:
\begin{enumerate}[leftmargin=8mm]
\item A rigorous \textbf{Train-on-Simulation, Test-on-Real} protocol, including standardized feature schema, splits, metrics, and uncertainty reporting aligned with ASHRAE~14 and IPMVP.
\item A \textbf{hybrid modeling stack} combining tabular gradient boosting with physics-derived features, domain-adaptive reweighting, and conformal prediction for risk-aware decisions.
\item \textbf{Evidence} that modest calibration using short post-retrofit measurements substantially improves real-world fidelity while preserving scalability.
\end{enumerate}

\section{Related Work}
\paragraph{Physics-based and hybrid approaches.} Building energy modeling has long relied on detailed simulation~\citep{crawley2001energyplus,klein2017trnsys,wang2015modelica}. Recent work integrates machine learning with physics-informed priors or gray-box structures~\citep{drgona2020all,heinen2022flexibility}. 
\paragraph{Data-driven prediction and transfer.} For tabular retrofit prediction, ensemble learners and deep networks have shown promise~\citep{ahmad2017review,li2021review,smarra2018data}. Transfer learning and domain adaptation for buildings are emerging~\citep{hong2020transfer,mahnke2022transfer,li2022domain}, yet systematic Sim2Real evaluation remains limited. 
\paragraph{Measurement and verification (M\&V).} Robust validation is anchored in ASHRAE Guideline~14 and IPMVP~\citep{ashrae2014guideline,ipmvp2012}. Public stock models (e.g., ResStock) and EU datasets (e.g., iNSPiRe) enable pre-training but rarely include long-horizon post-retrofit monitoring~\citep{resstock2017,wolf2014inspire}.

\section{Methodology}
\subsection{Data Regimes and Splits}
We adopt a two-regime setup: (A) \emph{Simulated} (training and in-domain testing) drawn from the iNSPiRe and ResStock corpora, and (B) \emph{Real} (out-of-domain testing) consisting of public retrofit case studies with submetering and IEQ measurements. To ensure a clean generalisation test, we use building-disjoint and retrofit–package–disjoint splits between training and testing. The feature set includes building typology, vintage, climate (K\"oppen class and heating/cooling degree days), envelope parameters (U/R-values and glazing ratios), HVAC system efficiencies, and baseline use intensity. Targets include both relative site energy savings expressed in percentage points and absolute end‑use deltas measured in \si{kWh}. Unless otherwise stated, mean absolute error (MAE) and root‑mean‑square error (RMSE) are reported in \si{kWh\per month} per building. Relative metrics (e.g., CV(RMSE), NMBE) follow the definitions in ASHRAE~14 and are computed at monthly granularity.
\subsection{Hybrid Model Stack}
Our hybrid stack combines gradient boosting (XGBoost/LightGBM) with domain knowledge and adaptation. We impose monotonic constraints on physically monotonic attributes (e.g., increased insulation should not increase heating load) and optionally compare against feed‑forward networks in our ablations. Physics proxies—such as heating and cooling degree days and steady‑state heat‑loss coefficients—augment the raw features. To mitigate covariate shift between simulated and real datasets, we estimate propensity scores using a logistic regression over building typology, climate zone, envelope parameters and baseline intensity. These scores form importance weights that reweight the simulated training distribution; to control variance we truncate weights at the 99th percentile and normalise them to sum to one. A lightweight calibration step further adapts the model to each retrofit by fitting a ridge regressor to a short post‑retrofit window (default four weeks). We explore sensitivity to the calibration window length (1–8~weeks) and to the propensity model in the supplementary material.
\subsection{Uncertainty and Error Decomposition}
We report MAE, RMSE and $R^2$ in the units described above, along with the coverage and width of conformal prediction intervals. To quantify where errors arise, we decompose predictive error into (i) covariate shift between the simulation and real regimes, (ii) label noise from sensor error and baseline drift, and (iii) unmodelled concurrent interventions. Prediction intervals are constructed using split conformal calibration across buildings; we evaluate both global and group‑stratified splits (e.g., by building type) and present empirical coverage versus nominal values. We additionally provide per‑feature SHAP attributions to interrogate the contribution of physics proxies and report sensitivity to occupant‑related proxies.
\subsection{Evaluation Protocol}
In‑domain performance is evaluated with a $5\times$ cross‑validation across buildings, while out‑of‑domain performance is assessed via building‑level leave‑one‑project‑out evaluation on the real datasets. To comply with measurement and verification practice, we compute CV(RMSE) and NMBE at monthly granularity following ASHRAE~14 definitions. All metrics are aggregated per building, and statistical significance of differences between models is assessed using paired $t$‑tests and bootstrap confidence intervals across buildings. Supplementary tables report fairness analyses by building type, climate zone and retrofit package.

\section{Experiments \& Results}
\subsection{Baselines}
Elastic Net, Random Forest, XGBoost, LightGBM, and MLP; plus two physics-inspired baselines: (i) static UA-based estimator; (ii) calibrated simulation deltas.

\subsection{Main Findings}
(1) On simulated hold‑outs, boosting models achieve $\mathrm{MAE}<3$~percentage points for relative savings. (2) On real projects, naïve models underperform due to covariate shift; our hybridisation reduces absolute MAE by 20--35~\% (measured in kWh/month per building) relative to pure ML baselines. (3) Short (\mbox{$\leq$4~week}) post‑retrofit calibration further closes residual bias while preserving generality.

\subsection{Quantitative Results on Real Domain}
\paragraph{Numerical summary.} Against the plain GBM baseline (MAE=127.95~kWh/month, RMSE=151.31~kWh/month, $R^2$=-2.44), the proposed \emph{Hybrid} reduces MAE to 58.25~kWh/month and RMSE to 76.97~kWh/month, corresponding to relative improvements of 54.47~\% and 49.13~\%, respectively. The coefficient of determination increases from -2.44 to 0.10 (absolute $\Delta$=2.54).
\label{subsec:real_results}
\begin{table}[t]
  \centering
  \caption{Main-task performance on real projects (LOPO across buildings). Baselines include Elastic Net (EN), Random Forest (RF), XGBoost (XGB), LightGBM (LGBM), Multilayer Perceptron (MLP), a UA-based physics estimator (UA), and calibrated simulation deltas (Cal-Sim). Hybrid is our proposed stack. Metrics: MAE and RMSE measured in kWh/month per building, coefficient of determination ($R^2$), CV(RMSE), and NMBE.}
  \label{tab:real_results}
  \input{../tabs/table3_hybrid.tex}
\end{table}

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% 4.4 Error Analysis and Bias Diagnostics
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\subsection{Error Analysis and Bias Diagnostics}
\label{subsec:error_analysis}
\paragraph{Aggregate reliability.}
Post‑calibration on the real domain further reduces MAE and RMSE relative to the uncalibrated hybrid and modestly improves $R^2$. The 90~\% conformal intervals achieve empirical coverage close to their nominal level with widths proportionate to the building‑level energy consumption, indicating well‑calibrated uncertainty under Sim$\rightarrow$Real deployment.

\paragraph{Residual distribution and scatter.}
Figure~\ref{fig:hybrid-error-diagnostics} shows that residuals are centered around zero with shortened left-tail mass; the predicted--actual scatter aligns closely with the identity line, suggesting reduced systematic bias after hybridization and light field calibration.

\begin{figure}[t]
\centering
\begin{subfigure}{0.48\linewidth}
  \includegraphics[width=\linewidth]{../figs/residual_hist_hybrid.png}
  \caption{Hybrid residuals}\label{fig:resid-hist-from-calib}
\end{subfigure}\hfill
\begin{subfigure}{0.48\linewidth}
  \includegraphics[width=\linewidth]{../figs/scatter_hybrid.png}
  \caption{Predicted vs.\ actual}\label{fig:scatter-from-calib}
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\caption{Error diagnostics under Train-on-Sim, Calibrate-on-Real.}
\label{fig:hybrid-error-diagnostics}
\end{figure}

\paragraph{Coverage vs.\ width trade-off.}
Figure~\ref{fig:conformal-reliability} summarizes conformal reliability: empirical coverage closely tracks nominal across 0.6--0.95, and the coverage--width curve quantifies the cost of higher protection.

% Conditionally include conformal reliability figures if available
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\centering
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  \caption{Reliability: nominal vs.\ empirical}\label{fig:reliability}
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\begin{subfigure}{0.48\linewidth}
  \includegraphics[width=\linewidth]{../figs/coverage_width_tradeoff.png}
  \caption{Coverage--width trade-off}\label{fig:cov-width}
\end{subfigure}
\caption{Conformal uncertainty diagnostics on real projects.}
\label{fig:conformal-reliability}
\end{figure}
}{}

\paragraph{Summary tables.}
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\subsection{Dataset Shift Diagnostics}
\label{subsec:shift}
We quantify Sim$\rightarrow$Real covariate shift across numeric and categorical features to motivate hybridization and post-retrofit calibration. Following industry practice, we flag \textbf{PSI}$>\num{0.25}$ as \emph{strong shift}. Tables~\ref{tab:shift_numeric_ci}--\ref{tab:shift_categorical_ci} rank the most shifted features; we also provide a marginal illustration on floor area (Figure~\ref{fig:shift-floor-area}).

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\begin{figure}[htbp]
\centering
\includegraphics[width=.6\linewidth]{../figs/shift_floor_area_m2.png}
\caption{Illustrative marginal shift on \texttt{floor\_area\_m2}.}
\label{fig:shift-floor-area}
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\section{Discussion}
We demonstrate that simple, well-regularized tabular models—when augmented with physics proxies and minimal field calibration—can deliver robust Sim2Real performance without heavy digital twin infrastructure. Remaining challenges include sparse IEQ coverage, occupancy dynamics, and weather normalization under climate trends. Future work: multi-task learning across energy and IEQ, causal adjustment for concurrent interventions, and open benchmarks with standardized M\&V artifacts.

\section{Conclusion}
We provide a reproducible, hybrid framework that quantifies and narrows the retrofit Sim2Real gap and a protocol aligned with industry verification standards. Our results support trustworthy, scalable pre-screening of retrofit portfolios and risk-aware investment decisions.

\section*{AI Contribution Disclosure}
This manuscript's research ideation, literature scoping, methodology drafting, LaTeX structuring, and language polishing were assisted by an AI system. The AI proposed the Sim2Real protocol, suggested hybrid modeling (physics proxies + boosting + conformal UQ), drafted the experiment card, organized the statements herein, and produced the initial .bib. All data curation, code implementation, figure generation, and final claims were reviewed and validated by the human authors.

\section*{Responsible AI Statement}
We anticipate positive impacts in improving retrofit targeting and reducing wasted investments. Risks include misuse of predictions without M\&V, bias against under-instrumented buildings, and privacy issues in monitoring. Mitigations: (i) require uncertainty reporting and M\&V-aligned metrics, (ii) provide calibration guidance for low-sensor settings, (iii) enforce data minimization and anonymization, and (iv) open-sourcing code and benchmarks for scrutiny.

\section*{Reproducibility Statement}
All code, configuration files, and experiment logs will be released under an open-source license. We provide data loaders that map iNSPiRe/ResStock schemas to our feature space, scripts for domain reweighting and conformal UQ, and seeds for CV splits. A README details environment setup, hyperparameters, and exact commands to reproduce results; a \texttt{reproducibility\_checklist.md} follows Agents4Science guidance.

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