CVAE + LCA

Deep LearningNavier LabGenerative ModelingSustainability

The Problem

The construction sector is one of the largest contributors to global emissions, yet early-stage design still relies mostly on intuition and experience. Life Cycle Assessment — the rigorous accounting of a building's environmental impact from material extraction to demolition — is computationally expensive and arrives too late in the process to meaningfully shape form. My goal was to reframe sustainable form-finding strictly as a machine learning challenge: embed the full cost of a design decision into the generative process itself.

The Approach

The project has two distinct phases, corresponding to the forward and inverse problems.

Surrogate modeling. I first trained a Multilayer Perceptron on a dataset of over 90,000 parametrically generated buildings to predict eight LCA indicators — embodied carbon, energy use, water consumption, and others — directly from geometric and material parameters. This surrogate bypasses costly physical simulation entirely, making real-time evaluation tractable.

The overall pipeline — Conditional Variational Autoencoder for structural design with environmental constraints

Inverse design. With the forward problem solved, I tackled the harder question: given a set of environmental constraints, what geometries satisfy them? I trained a Conditional Variational Autoencoder conditioned on those eight indicators simultaneously. The model is trained by maximizing the evidence lower bound:

\mathcal{L}(\theta, \phi;\, \mathbf{x}, \mathbf{c}) = \mathbb{E}_{q_\phi(\mathbf{z}|\mathbf{x},\mathbf{c})}\!\left[\log p_\theta(\mathbf{x}|\mathbf{z},\mathbf{c})\right] - D_\mathrm{KL}\!\left(q_\phi(\mathbf{z}|\mathbf{x},\mathbf{c})\;\|\;p(\mathbf{z})\right)

where $\mathbf{x}$ is the structural configuration, $\mathbf{c} \in \mathbb{R}^8$ is the environmental condition vector, and $\mathbf{z}$ is the latent variable. Rather than optimizing toward a single objective, the CVAE learns to propose diverse structural configurations that live within a specified environmental envelope — a generative model for the feasible set.

Evaluation

Because no single design is optimal across all eight dimensions simultaneously, performance is evaluated on the Pareto front: the set of configurations for which no indicator can be improved without degrading another. The quality of the generative model is then measured by the hypervolume indicator $\mathcal{H}$ , which captures the volume of objective space dominated by the front:

\mathcal{H}(F, \mathbf{r}) = \lambda\!\left(\bigcup_{\mathbf{f} \in F} [\mathbf{f},\, \mathbf{r}]\right)

where $F$ is the Pareto front, $\mathbf{r}$ is a reference point, and $\lambda$ denotes the Lebesgue measure. A higher hypervolume means the model covers more of the achievable trade-off surface.

Exploring the latent space reveals the continuous topological transitions between material choices, structural geometries, and environmental profiles — making trade-offs legible and navigable. The result is an interactive, data-driven tool that gives designers direct access to the sustainable region of the design space, at the moment when it still matters.