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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{}

\begin{document}
\maketitle

\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) sourced from iNSPiRe and ResStock schemas; (B) \emph{Real} (out-of-domain testing) from public retrofit case studies with submetering and IEQ. Splits are building-disjoint and retrofit-package disjoint. Features include typology, vintage, climate (K\"oppen and HDD/CDD), envelope parameters (U/R-values, glazing ratios), HVAC system efficiencies, and baseline use intensity. Targets: site energy savings (\%), end-use deltas (kWh), and IEQ proxies.
\subsection{Hybrid Model Stack}
We use gradient boosting (XGBoost/LightGBM) with monotone constraints on physically monotonic attributes (e.g., higher insulation $\rightarrow$ non-increasing heating load), plus optional feed-forward nets for ablations. Physics proxies (degree-days, steady-state heat-loss coefficients) augment raw features. Domain-adaptive importance reweighting is applied via propensity scores estimated on a joint representation; calibration uses shallow ridge regressors fit to short-horizon post-retrofit readings.
\subsection{Uncertainty and Error Decomposition}
We report MAE/RMSE/$R^2$, plus coverage/width of conformal intervals. Errors are decomposed into (i) covariate shift, (ii) label noise (sensor and baseline drift), and (iii) unmodeled interventions. We provide per-feature SHAP attributions and sensitivity to occupant-related proxies.
\subsection{Evaluation Protocol}
In-domain: $5\times$CV across buildings; Out-of-domain: building-level leave-one-project-out on real datasets. M\&V compliance: CV(RMSE) and NMBE at monthly/weekly granularity. Statistical testing uses paired t-tests and bootstrap CIs across buildings.

\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 $\mathrm{MAE}\!<\!3$\,pp for savings(\%). (2) On real projects, naive models underperform due to shift; hybridization reduces MAE by 20--35\% versus pure ML. (3) Short ($\leq$4~weeks) post-retrofit calibration closes most residual bias while preserving generality.

\subsection{Quantitative Results on Real Domain}
\paragraph{Numerical summary.} Against the plain GBM baseline (MAE=127.95, RMSE=151.31, $R^2$=-2.44), the proposed \emph{Hybrid} reduces MAE to 58.25 and RMSE to 76.97, 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, RMSE, $R^2$, CV(RMSE), NMBE.}
  \label{tab:real_results}
  \input{../tabs/table3_hybrid.tex}
\end{table}

% ============================
% 4.4 Error Analysis and Bias Diagnostics
% ============================
\subsection{4.4\quad Error Analysis and Bias Diagnostics}
\label{subsec:error_analysis}
\paragraph{Aggregate reliability.}
Post-calibration on the real domain yields \textbf{MAE}=\num{6501.2}, \textbf{RMSE}=\num{9471.5}, and $R^2=\num{0.1695}$. The 90\% conformal intervals achieve empirical coverage of \textbf{0.899} with mean width \textbf{\num{27323.4}}, indicating well-calibrated uncertainty under the 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}
\end{subfigure}
\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.

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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{4.5\quad 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}[t]
\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}
\end{figure}


\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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