%% ============================================================================
%% ELSEVIER JOURNAL TEMPLATE (Building and Environment / Automation in Construction)
%% Title: Coupled Plan-to-Facade Optimization for Microclimatic Comfort in 
%%        Tropical Tube Houses Using a Multi-Fidelity Physics-Guided Graph-CVAE
%% ============================================================================
\documentclass[5p,times,twocolumn]{elsarticle}

\usepackage{amsmath,amssymb,amsfonts}
\usepackage{algorithmic}
\usepackage{graphicx}
\usepackage{textcomp}
\usepackage{xcolor}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{siunitx}
\usepackage{hyperref}

\journal{Building and Environment}

\begin{document}

\begin{frontmatter}

\title{Coupled Plan-to-Facade Optimization for Microclimatic Comfort in Tropical Tube Houses Using a Multi-Fidelity Physics-Guided Graph-CVAE}

\author[inst1]{Nguyen Thanh Hoang\corref{cor1}}
\ead{hoangnt@dau.edu.vn}
\cortext[cor1]{Corresponding author}

\affiliation[inst1]{organization={Da Nang Architecture University (DAU)},
            city={Da Nang},
            postcode={550000}, 
            country={Vietnam}}

\begin{abstract}
Rapid post-1986 (\textit{Doi Moi}) urbanization in coastal Vietnamese cities such as Da Nang has proliferated high-density, narrow-frontage ``tube houses'' (\textit{nha ong}, width $W \in [3.5, 6.0]\,\text{m}$, depth $L \in [15, 25]\,\text{m}$) flanked by three adiabatic party walls. The prevailing separation between internal spatial zoning and fully glazed West/East facades triggers severe solar overheating ($\text{SHG} > 110\,\text{kWh/m}^2\cdot\text{yr}$) and middle-zone airflow stagnation ($\text{ACH} < 2.1\,\text{h}^{-1}$). Conversely, post-1954 Vietnamese Modernist architecture in both North and South Vietnam evolved sophisticated passive ``morpho-microclimatic DNA''---integrating multi-layered \textit{brise-soleil}, porous \textit{claustra} screens, deep buffer verandas, and buoyancy-driven lightwells. This paper proposes a coupled Plan-to-Facade generative optimization framework powered by a Dual-ONNX neural pipeline. First, a \textbf{Multi-Task Tropical Surrogate} combines a 2.5D Spatial Graph Convolutional Network ($8 \times 6$ node features and $8 \times 8$ adjacency matrix) with a 14-parameter facade encoder to predict four annual performance metrics ($\text{ACH}$, $\text{sDA}_{300/50\%}$, $\text{SHG}$, and Adaptive Thermal Comfort $\text{ATC}$) alongside a 16-mode Proper Orthogonal Decomposition (POD) longitudinal airflow field. Trained on a multi-fidelity dataset of 15,000 EnergyPlus/AirflowNetwork simulations and 600 OpenFOAM RANS CFD cases calibrated against 12 monitored tube houses in Da Nang (meeting ASHRAE Guideline 14 criteria), the surrogate achieves $R^2 \in [0.964, 0.981]$ with a $1.8\,\text{ms}$ inference latency. Second, a \textbf{Physics-Guided Graph-CVAE} trained via Backpropagation-Through-Surrogate (BPTS) synthesizes buildable 2.5D spatial graphs and porous facade vectors under Constraint Satisfaction Problem (CSP) geometric filters. Co-simulation over 8,760 hours via an FMI 2.0 Functional Mock-up Unit (\texttt{onnx2fmu}) demonstrates that generated designs increase natural ventilation to $9.8\,\text{h}^{-1}$ ($+366\%$), reduce solar heat gain by $64.2\%$, extend annual passive comfort hours to $84.6\%$ under ASHRAE 55, and lower cooling loads by $48.2\%$.
\end{abstract}

\begin{keyword}
Vietnamese Modernist Architecture \sep Tropical Tube House \sep Physics-Guided Graph-CVAE \sep CFD Surrogate Modeling \sep Proper Orthogonal Decomposition \sep Coupled Plan-to-Facade Optimization
\end{keyword}

\end{frontmatter}

%% ============================================================================
%% 1. INTRODUCTION
%% ============================================================================
\section{Introduction}
\label{sec:intro}

\subsection{Historical Context: Post-1954 Vietnamese Modernism and the Post-1986 Tube House Crisis}
Following the 1954 Geneva Accords, architectural development in Vietnam bifurcated into two distinct political and economic spheres across the 17th parallel, yet converged remarkably around passive tropical adaptation \cite{schenck2020southern,schwenkel2020building}. In the North, state-led Socialist Modernism produced monumental public buildings and collective housing districts (\textit{Khu tap the} Kim Lien, Trung Tu) designed by architects trained in the Indochina College of Fine Arts and Soviet-bloc academies. Constrained by severe post-war material shortages and the absence of mechanical air-conditioning, Northern architects engineered deep perimeter loggias ($1.2\text{--}1.8\,\text{m}$), thick lime-plastered brick walls, vertical concrete fins, and cross-ventilated double-loaded plans. Simultaneously, in the South, architects such as Ngo Viet Thu, Nguyen Quang Nhac, and Le Van Lam synthesized French Beaux-Arts spatial composition with Tropical Modernism, pioneering decorative double-skin concrete \textit{brise-soleil}, glazed ceramic breeze blocks (\textit{gach thong gio}), and central courtyards that functioned as aerodynamic pressure regulators.

However, the economic liberalization of 1986 (\textit{Doi Moi}) shifted urban housing production toward self-built, high-density ``tube houses'' (\textit{nha ong}) occupying narrow, deep parcels ($W \in [3.5, 6.0]\,\text{m}$, $L \in [15.0, 25.0]\,\text{m}$, $N_{\text{floors}} \in [3, 5]$, aspect ratio $L/W > 4.0$). Flanked on three sides by contiguous neighboring party walls, these dwellings rely exclusively on the narrow front facade and roof aperture for environmental exchange. Contemporary tube houses frequently adopt unshaded curtain-wall glazing and omit internal lightwells to maximize floor area, resulting in severe solar heat accumulation, dark core zones ($\text{sDA}_{300/50\%} < 25\%$), and stagnant indoor air ($\text{ACH} < 2.1\,\text{h}^{-1}$), forcing heavy reliance on split-system air conditioning \cite{nguyen2011investigation}.

\subsection{Research Gap and Coupled Plan-to-Facade Hypothesis}
Existing computational architectural studies predominantly treat floorplan generation \cite{nauata2021house} and facade shading optimization as decoupled problems. In a tropical tube house, however, environmental performance is governed by a strictly \textbf{coupled thermo-aerodynamic mechanism}: a porous \textit{brise-soleil} or breeze-block facade only induces effective cross-ventilation if paired with an internal 2.5D spatial topology---specifically a continuous pressure pathway linking the front loggia, open-plan living zone, central lightwell (\textit{gieng troi}), and rear ventilation shaft. Conversely, optimizing an internal courtyard without calibrating facade porosity ($\phi$) and louver angle ($\theta_{\text{louver}}$) against solar azimuth exposes the building core to direct radiation or blocks incoming coastal sea breezes.

While coupled Computational Fluid Dynamics (CFD) and Radiance daylighting simulations can evaluate this interaction accurately, a single high-fidelity simulation requires $45\text{--}180\,\text{minutes}$, precluding real-time generative design exploration. To bridge this gap, this study formulates three primary contributions:
\begin{enumerate}
    \item \textbf{Empirical Baseline and Heritage Digitization}: Field monitoring of 12 representative tube houses in Da Nang across four tropical monsoon climate regimes, combined with a 2.5D + 14D parametric encoding of Vietnamese Modernist morpho-microclimatic DNA.
    \item \textbf{Multi-Fidelity Dual-ONNX Neural Architecture}: A coupled Graph-to-Performance Surrogate (\texttt{MultiTaskTropicalSurrogate}) predicting scalar comfort metrics and 16 POD airflow modes in $1.8\,\text{ms}$, paired with a Physics-Guided Graph-CVAE (\texttt{CoupledTubeHouseGenerator}) trained via differentiable Backpropagation-Through-Surrogate (BPTS).
    \item \textbf{Dynamic Co-Simulation Validation}: Seamless integration of the trained neural models into Grasshopper 3D and EnergyPlus 8,760-hour annual co-simulation via the Functional Mock-up Interface (\texttt{onnx2fmu}).
\end{enumerate}

%% ============================================================================
%% 2. METHODOLOGY
%% ============================================================================
\section{Methodology}
\label{sec:method}

\subsection{Climatic Context of Da Nang and Empirical Field Monitoring}
Da Nang ($16.05^\circ\text{N}$, $108.20^\circ\text{E}$) exhibits a Tropical Monsoon climate (Aw/Am) characterized by four critical microclimatic regimes:
\begin{itemize}
    \item \textbf{Regime I (Dry-Season Foehn Wind, May--August)}: Hot, dry Southwest ``Lao winds'' with peak ambient temperatures $T_{\text{amb}} = 37\text{--}40^\circ\text{C}$, relative humidity $\text{RH} = 45\text{--}55\%$, and intense West solar irradiance ($I_{\text{global}} > 920\,\text{W/m}^2$).
    \item \textbf{Regime II (Coastal East/Southeast Sea Breeze)}: Diurnal marine breezes ($v_{\text{wind}} = 3.2\text{--}5.5\,\text{m/s}$, $T_{\text{amb}} = 28\text{--}31^\circ\text{C}$) providing high natural cooling potential.
    \item \textbf{Regime III (Equinox Shoulder Seasons, March--April)}: Moderate temperatures ($25\text{--}29^\circ\text{C}$) ideal for full-time passive comfort.
    \item \textbf{Regime IV (Northeast Monsoon \& Rain, September--December)}: High humidity ($\text{RH} > 85\%$) and driving rain requiring inclined louver protection.
\end{itemize}

To establish empirical ground truth, 12 existing tube houses in Hai Chau, Thanh Khe, and Son Tra districts (3 orientations: West/Northwest, East/Southeast, South; 4 typologies per orientation) were instrumented over 14-day campaigns in both dry and wet seasons. Five synchronized sensor nodes were deployed per house: $\text{Node } S_0$ (Roof Weather Station), $\text{Node } S_1$ (Front Buffer Loggia), $\text{Node } S_2$ (1st-Floor Living Room), $\text{Node } S_3$ (Central Lightwell at 2nd/3rd Floor), and $\text{Node } S_4$ (Top-Floor Front Bedroom). Mean Radiant Temperature ($T_{\text{mrt}}$, $^{\circ}\text{C}$) is derived from black-globe measurements ($D_g = 0.15\,\text{m}$, $\varepsilon_g = 0.95$) according to ISO 7726 \cite{iso7726}:
\begin{equation}
T_{\text{mrt}} = \left[ (T_g + 273.15)^4 + \frac{1.1 \times 10^8 \, v_a^{0.6}}{\varepsilon_g \, D_g^{0.4}} (T_g - T_a) \right]^{1/4} - 273.15
\label{eq:tmrt}
\end{equation}
Operative temperature ($T_{\text{op}}$) and the ASHRAE 55-2023 \cite{ashrae55} 80\% acceptability upper limit ($T_{\text{upper},80\%}$, including the elevated air-speed cooling credit $\Delta T_v \in [1.2, 2.2]\,^\circ\text{C}$ when $v_a \in [0.6, 1.2]\,\text{m/s}$) are computed as:
\begin{equation}
T_{\text{op}} = A \cdot T_a + (1 - A) \cdot T_{\text{mrt}}, \quad T_{\text{upper},80\%} = 0.31 \, T_{\text{pma(out)}} + 21.3 + \Delta T_v
\label{eq:top}
\end{equation}

\begin{table*}[t]
\centering
\caption{Parametric Design Space: Coupled 2.5D Spatial Graph ($H_v$) and 14D Tropical Modernist Facade Vector ($X_{\text{facade}}$).}
\label{tab:design_space}
\begin{tabular}{@{}llll@{}}
\toprule
\textbf{Category} & \textbf{Symbol / Tensor} & \textbf{Parameter Description} & \textbf{Range / Domain} \\ \midrule
\multirow{2}{*}{Site Context ($C_{\text{site}}$)} & $W_{\text{plot}}, L_{\text{plot}}, N_{\text{flr}}$ & Plot width, length, and number of stories & $[3.5, 6.0]\,\text{m}, [15, 25]\,\text{m}, \{3, 4, 5\}$ \\
 & $\alpha_{\text{azi}}, W_{\text{road}}, T_{\text{amb}}, v_{\text{wind}}, I_{\text{sol}}$ & Orientation, street width, and microclimate boundary & $[0^\circ, 360^\circ], [4, 20]\,\text{m}, [24, 40]^\circ\text{C}$ \\ \midrule
\multirow{2}{*}{2.5D Plan Graph ($G$)} & $H_v \in \mathbb{R}^{8 \times 6}$ & 8 functional zones $\times (\Delta x, \Delta y, \Delta z, A_{\text{ratio}}, z_{\text{level}}, \kappa_{\text{open}})$ & Normalized $[0, 1]^{8 \times 6}$ \\
 & $A \in \{0,1\}^{8 \times 8}$ & Horizontal door/open-plan \& vertical stack adjacency & Symmetric binary graph \\ \midrule
\multirow{4}{*}{Facade DNA ($X_{\text{facade}}$)} & $d_{\text{loggia}}, h_{\text{overhang}}$ & Front loggia buffer depth \& canopy projection & $[0.4, 2.4]\,\text{m}, [0.3, 1.8]\,\text{m}$ \\
 & $\phi_{\text{breeze}}, \theta_{\text{louver}}, s_{\text{b}}$ & Porosity, louver tilt/azimuth angle, blade spacing/depth & $[0.15, 0.75], [-60^\circ, 60^\circ], [0.1, 0.6]$ \\
 & $\text{WWR}, d_{\text{cavity}}, \rho_{\text{alb}}$ & Window-to-wall ratio, double-skin gap, surface albedo & $[0.20, 0.70], [0.2, 1.2]\,\text{m}, [0.3, 0.85]$ \\
 & $A_{\text{atrium}}, h_{\text{vent}}, f_{\text{green}}$ & Lightwell ratio, roof vent height, green balcony fraction & $[0.04, 0.18], [0.4, 1.5]\,\text{m}, [0.0, 0.6]$ \\ \bottomrule
\end{tabular}
\end{table*}

\subsection{Coupled 2.5D Spatial Graph and Facade Tensor Formulation}
Each tube house candidate is represented as a coupled tuple $(C_{\text{site}}, G, X_{\text{facade}})$ summarized in Table~\ref{tab:design_space}. The internal layout is abstracted as an 8-node attributed spatial graph $G = (V, E, H_v, A)$, where the 8 canonical nodes represent: $v_0$ (Front Buffer Loggia), $v_1$ (Living Room T1), $v_2$ (Staircase Core), $v_3$ (Central Lightwell / Atrium), $v_4$ (Kitchen \& Dining T1), $v_5$ (Front Bedrooms T2--Tn), $v_6$ (Rear Bedrooms T2--Tn), and $v_7$ (Rear Ventilation Yard). To prevent geometrically invalid layouts prior to neural evaluation, a Constraint Satisfaction Problem (CSP) filter enforces usable area efficiency $\eta_{\text{usable}} = A_{\text{habitable}}/A_{\text{gross}} \ge 0.82$, minimum habitable room dimension $L_{\text{room,min}} \ge 3.2\,\text{m}$, and mandatory ventilation connectivity for all bedrooms ($\sum_j A_{i,j} \kappa_{\text{open},j} > 0$).

\subsection{Multi-Fidelity Simulation and POD Reduced-Order Airflow}
To reconcile dataset scale with CFD accuracy, a two-tier Multi-Fidelity sampling strategy via Latin Hypercube Sampling (LHS) is implemented:
\begin{enumerate}
    \item \textbf{Low-Fidelity Tier ($N_{\text{LF}} = 15,000$)}: Evaluated via Grasshopper Honeybee EnergyPlus AirflowNetwork (AFN) and Radiance annual daylighting ($\text{sDA}_{300/50\%}$).
    \item \textbf{High-Fidelity Tier ($N_{\text{HF}} = 600$)}: Evaluated via 3D Steady-State RANS OpenFOAM (`buoyantSimpleFoam`, RNG $k$--$\varepsilon$ turbulence with Boussinesq thermal buoyancy) to capture coupled wind-driven and stack-effect velocity fields $\mathbf{u}(\mathbf{x})$.
\end{enumerate}

Simulation models are calibrated against the 12 field-monitored tube houses in accordance with ASHRAE Guideline 14-2014 \cite{ashrae2014guideline14} using Normalized Mean Bias Error ($\text{NMBE} \in [-10\%, +10\%]$) and Coefficient of Variation of the Root Mean Square Error ($\text{CV(RMSE)} \le 30\%$):
\begin{equation}
\text{NMBE} = \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)}{(n - p) \bar{y}} \times 100\%, \quad \text{CV(RMSE)} = \frac{1}{\bar{y}} \sqrt{\frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{n - p}} \times 100\%
\label{eq:ashrae14}
\end{equation}

Following Zhao et al.~\cite{zhao2021cfd}, the 2.5D longitudinal section velocity fields $\mathbf{U} \in \mathbb{R}^{M \times N_{\text{HF}}}$ are decomposed via Singular Value Decomposition (SVD) into $K=16$ orthogonal spatial modes $\Phi_k(\mathbf{x})$ capturing $97.4\%$ of the total kinetic energy:
\begin{equation}
\mathbf{u}(\mathbf{x}; G, X_{\text{facade}}) \approx \bar{\mathbf{u}}(\mathbf{x}) + \sum_{k=1}^{16} \alpha_k(G, X_{\text{facade}}) \, \Phi_k(\mathbf{x})
\label{eq:pod}
\end{equation}

\subsection{Dual-ONNX Architecture: Multi-Task Surrogate and Physics-Guided Graph-CVAE}
The first neural module, \texttt{MultiTaskTropicalSurrogate} ($f_\theta$), processes $(H_v, A)$ through two Graph Convolutional message-passing layers:
\begin{equation}
H^{(l+1)} = \text{GELU}\left( \tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2} H^{(l)} W_g^{(l)} \right), \quad \mathbf{z}_{\text{plan}} = \frac{1}{|V|} \sum_{i=1}^{8} H_i^{(2)}
\label{eq:gcn}
\end{equation}
Concatenating $\mathbf{z}_{\text{plan}}$ with MLP embeddings of $X_{\text{facade}}$ and $C_{\text{site}}$ feeds a shared Residual MLP trunk that predicts the 4 scalar metrics $\hat{Y}_{\text{perf}} = [\widehat{\text{ACH}}, \widehat{\text{sDA}}, \widehat{\text{SHG}}, \widehat{\text{ATC}}]$ and the 16 POD coefficients $\hat{\boldsymbol{\alpha}}_{\text{POD}} \in \mathbb{R}^{16}$. To balance multi-task gradients automatically, homoscedastic uncertainty weighting \cite{kendall2018multi} is employed:
\begin{equation}
\mathcal{L}_{\text{surrogate}} = \sum_{m=1}^{4} \left( \frac{1}{2\sigma_m^2} \| y_m - \hat{y}_m \|_2^2 + \log \sigma_m \right) + \frac{1}{2\sigma_{\text{POD}}^2} \| \boldsymbol{\alpha}_{\text{POD}} - \hat{\boldsymbol{\alpha}}_{\text{POD}} \|_2^2
\label{eq:homoscedastic}
\end{equation}

The second module, \texttt{CoupledTubeHouseGenerator} ($g_\phi$), is a Conditional Graph-VAE conditioned on $(C_{\text{site}}, Y_{\text{target}})$. During training, weights $\theta$ of $f_\theta$ are frozen, and $g_\phi$ is optimized end-to-end via Backpropagation-Through-Surrogate (BPTS):
\begin{equation}
\mathcal{L}_{\text{total}} = \mathcal{L}_{\text{recon}} + \beta \, D_{\text{KL}}\big(q_\phi(Z) \,\|\, \mathcal{N}(0,I)\big) + \lambda_{\text{phys}} \mathcal{L}_{\text{physics}} + \lambda_{\text{CSP}} \mathcal{L}_{\text{CSP}}
\label{eq:cvae_loss}
\end{equation}
where $\mathcal{L}_{\text{physics}}$ penalizes under-ventilation, solar overheating, and stagnation in the central lightwell:
\begin{align}
\mathcal{L}_{\text{physics}} &= w_1 \text{ReLU}(8.0 - \widehat{\text{ACH}}) + w_2 \text{ReLU}(65.0 - \widehat{\text{sDA}}) \nonumber \\
&\quad + w_3 \frac{\widehat{\text{SHG}}}{100} + w_4 \text{ReLU}(80.0 - \widehat{\text{ATC}}) + w_5 \text{ReLU}(0.25 - \|\hat{\boldsymbol{\alpha}}_{\text{POD}}\|_2)
\label{eq:phys_loss}
\end{align}

%% ============================================================================
%% 3. RESULTS AND DISCUSSION
%% ============================================================================
\section{Results and Discussion}
\label{sec:results}

\subsection{Surrogate Model Accuracy and Computational Acceleration}
Table~\ref{tab:surrogate_perf} reports the out-of-sample evaluation of \texttt{MultiTaskTropicalSurrogate} on the held-out High-Fidelity CFD test set ($N_{\text{test}} = 120$). Across all four environmental metrics and the 16-mode POD velocity field, coefficients of determination exceed $R^2 = 0.964$, while $\text{NMBE}$ ($-1.4\%$ to $+1.8\%$) and $\text{CV(RMSE)}$ ($4.2\%$ to $6.8\%$) fall well within ASHRAE Guideline 14 thresholds. Crucially, the exported ONNX graph executes in $1.8\,\text{ms}$ per design candidate---representing a $1.5 \times 10^6$-fold speedup over coupled OpenFOAM + Radiance simulation.

\begin{table}[h]
\centering
\caption{Out-of-sample accuracy of \texttt{MultiTaskTropicalSurrogate} on High-Fidelity CFD & Radiance test set ($N=120$).}
\label{tab:surrogate_perf}
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Output Target} & $\mathbf{R^2}$ & \textbf{RMSE} & \textbf{NMBE (\%)} & \textbf{CV(RMSE) (\%)} \\ \midrule
$\text{ACH}$ ($\text{h}^{-1}$) & $0.974$ & $0.38$ & $+1.12\%$ & $5.41\%$ \\
$\text{sDA}_{300/50\%}$ (\%) & $0.981$ & $2.14$ & $-0.84\%$ & $4.18\%$ \\
$\text{SHG}$ ($\text{kWh/m}^2\text{yr}$) & $0.978$ & $2.65$ & $+1.45\%$ & $4.92\%$ \\
$\text{ATC}$ (\%) & $0.969$ & $1.92$ & $-1.18\%$ & $5.86\%$ \\
16-Mode POD $\mathbf{u}(\mathbf{x})$ & $0.964$ & $0.07\,\text{m/s}$ & $+1.76\%$ & $6.78\%$ \\ \bottomrule
\end{tabular}
\end{table}

\subsection{Morphological Sensitivity Analysis (SHAP) and North--South Convergence}
Game-theoretic Shapley Additive Explanations (SHAP) \cite{lundberg2017unified} reveal that natural ventilation ($\text{ACH}$) and adaptive thermal comfort ($\text{ATC}$) are governed primarily by the \textbf{cross-term interaction} between central lightwell ratio ($A_{\text{atrium}}$, $28.4\%$ contribution) and facade breeze-block porosity ($\phi_{\text{breeze}}$, $24.1\%$), followed by front loggia depth ($d_{\text{loggia}}$, $16.8\%$) and internal open-plan connectivity ($\kappa_{\text{open}}$, $14.2\%$). Notably, expanding $A_{\text{atrium}}$ from $4\%$ to $12\%$ increases $\text{ACH}$ by only $+1.4\,\text{h}^{-1}$ when $\phi_{\text{breeze}} < 0.20$, but yields $+5.8\,\text{h}^{-1}$ when paired with a porous double-skin facade ($\phi_{\text{breeze}} \ge 0.50$) and a $1.5\,\text{m}$ deep loggia---quantitatively validating the synergy between Northern loggia buffers and Southern porous \textit{claustra} screens.

\subsection{Annual 8,760-Hour Co-Simulation Verification via ONNX-to-FMU}
To verify dynamic annual performance under the Da Nang TMYx weather file, the surrogate ONNX graph was compiled into an FMI 2.0 Functional Mock-up Unit (\texttt{onnx2fmu}) and co-simulated with EnergyPlus over 8,760 hours for a benchmark $5 \times 20\,\text{m}$, 4-story West-facing tube house in Hai Chau District (Table~\ref{tab:fmu_annual}). Compared to the unshaded glazed Baseline, the Coupled Plan-to-Facade Graph-CVAE design reduces annual solar heat gain by $64.2\%$, boosts mean $\text{ACH}$ from $2.1$ to $9.8\,\text{h}^{-1}$, increases annual ASHRAE 55 passive comfort hours from $44.8\%$ to $84.6\%$ ($7,411\,\text{h/yr}$), and reduces annual HVAC cooling energy by $48.2\%$.

\begin{table}[h]
\centering
\caption{Annual 8,760-hour EnergyPlus + FMU co-simulation comparison for a West-facing $5\times 20\,\text{m}$ Da Nang tube house.}
\label{tab:fmu_annual}
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Design Strategy} & \textbf{ACH} ($\text{h}^{-1}$) & \textbf{SHG} ($\text{kWh/m}^2$) & \textbf{ATC} (\%) & \textbf{EUI}_{\text{cool}} ($\text{kWh/m}^2$) \\ \midrule
Baseline Glazed Tube House & $2.1$ & $118.4$ & $44.8\%$ & $78.6$ \\
Plan-Only Optimization & $4.8$ & $96.2$ & $58.2\%$ & $64.1$ \\
Facade-Only Optimization & $5.4$ & $46.8$ & $69.4\%$ & $51.3$ \\
\textbf{Coupled Graph-CVAE (Ours)} & $\mathbf{9.8}$ & $\mathbf{42.4}$ & $\mathbf{84.6\%}$ & $\mathbf{40.7}$ \\ \bottomrule
\end{tabular}
\end{table}

%% ============================================================================
%% 4. CONCLUSION
%% ============================================================================
\section{Conclusion}
\label{sec:conclusion}
By encoding the passive climatic wisdom of post-1954 Vietnamese Modernist architecture into a differentiable Coupled Plan-to-Facade Graph-CVAE and Multi-Fidelity POD Surrogate, this study resolves the long-standing computational bottleneck between spatial topology generation and environmental physics verification. Future work will extend the graph formulation to urban block-scale canyon microclimates and physical wind-tunnel prototyping.

\bibliographystyle{elsarticle-num}
\bibliography{references}

\end{document}