# A Unified Generative-Predictive Framework for Deterministic Inverse Design

arXiv: https://arxiv.org/abs/2512.15746 · HTML: https://mlsanity.com/paper/2512.15746/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Representational aspects of depth and conditioning in normalizing flows](https://mlsanity.com/paper/2010.01155/) (2020)
- [Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning](https://mlsanity.com/paper/2407.15887/) (2024)
- [An Introduction to Kernel and Operator Learning Methods for Homogenization by Self-consistent Clustering Analysis](https://mlsanity.com/paper/2212.00802/) (2022)
- [KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation](https://mlsanity.com/paper/2505.13315/) (2025)
- [Explainable Hierarchical Deep Learning Neural Networks (Ex-HiDeNN)](https://mlsanity.com/paper/2507.05498/) (2025)

## Built on by (most cited first, 3 of 3)

- [Agile Reinforcement Learning through Separable Neural Architecture and Applications](https://mlsanity.com/paper/2601.23225/) (2026)
- [Separable neural architectures as a primitive for unified predictive and generative intelligence](https://mlsanity.com/paper/2603.12244/) (2026)
- [Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications](https://mlsanity.com/paper/2606.14934/) (2026)

## Abstract (arXiv)

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 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 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 R2=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.