A Unified Generative-Predictive Framework for Deterministic Inverse Design

TL;DR

Janus presents a unified generative-predictive framework that jointly optimizes a latent space for decodability, predictive accuracy, and cycle-consistency, enabling deterministic inverse design with physics-informed guidance. By integrating a KHRONOS head within a learnable encoder-decoder latent manifold, Janus supports end-to-end generative inversion via a differentiable, low-dimensional latent space, dramatically reducing computational cost. Demonstrated on MNIST and a microstructure dataset targeting thermal conductivity, Janus achieves high forward accuracy, sub-5% pixelwise reconstruction errors, and near-1% relative error in inverse designs, with real-time inference achieved on modern GPUs. The work reveals a topologically organized latent geometry that enables smooth, monotonic property-driven traversals and diverse inverse designs, suggesting a practical pathway for rapid, interpretable inverse design in complex physical systems.

Abstract

Inverse design of heterogeneous material microstructures is a fundamentally ill-posed and famously computationally expensive problem. This is exacerbated by the high-dimensional design spaces associated with finely resolved images, multimodal input property streams, and a highly nonlinear forward physics. Whilst modern generative models excel at accurately modeling such complex forward behavior, most of them are not intrinsically structured to support fast, stable \emph{deterministic} inversion with a physics-informed bias. This work introduces Janus, a unified generative-predictive framework to address this problem. Janus couples a deep encoder-decoder architecture with a predictive KHRONOS head, a separable neural architecture. Topologically speaking, Janus learns a latent manifold simultaneously isometric for generative inversion and pruned for physical prediction; the joint objective inducing \emph{disentanglement} of the latent space. Janus is first validated on the MNIST dataset, demonstrating high-fidelity reconstruction, accurate classification and diverse generative inversion of all ten target classes. It is then applied to the inverse design of heterogeneous microstructures labeled with thermal conductivity. It achieves a forward prediction accuracy $R^2=0.98$ (2\% relative error) and sub-5\% pixelwise reconstruction error. Inverse solutions satisfy target properties to within $1\%$ relative error. Inverting a sweep through properties reveal smooth traversal of the latent manifold, and UMAP visualization confirms the emergence of a low-dimensional, disentangled manifold. By unifying prediction and generation within a single latent space, Janus enables real-time, physics-informed inverse microstructure generation at a lower computational cost typically associated with classical optimization-based approaches.

Figures (7)

• Figure 1: Overview of Janus' framework for inverse design of microstructure. During offline training (left), paired microstructure-property data are encoded into a jointly optimized shared latent space. Learned parameters are transferred into the online generation stage (right), where a target property is inversely mapped back to a latent code in the space. This code is then decoded by the trained decoder, resulting in a deterministic inverse generation.
• Figure 2: Forward (left) and inverse (right) architectures of Janus-C.
• Figure 3: Validation of generative inversion on the MNIST benchmark. Rows correspond to the target digit classes $\{0,\dots,9\}$ and columns display ten independent samples generated via parallel swarm inversion from random latent initalizations. The confidence of the KHRONOS head in each generation is also displayed inset within each.
• Figure 4: Training dynamics of Janus-C. (a) Regression learning curves with relative accuracy converging to 2.5%. (b) Reconstructive fidelity, measured by mean absolute error in pixel intensity, decreasing to sub 0.05. (c) Manifold stability in mean absolute terms for cycle-consistency and deep cycle losses.
• Figure 5: Generative inversion of microstructure. Top row: property sweep demonstrating deterministic targeting of microstructure for thermal conductivities of $k=15,25,35,45$ and $55$ (dimensionless). Bottom row: diversity analysis for a fixed target $35$ starting from five distinct starting seeds.