![[2602.14642] GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.14642] GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media
Summary
GenPANIS introduces a generative framework for solving forward and inverse PDE problems in multiphase media, enhancing accuracy and efficiency in modeling complex microstructures.
Why It Matters
This framework addresses challenges in multiphase media modeling by enabling gradient-based inference with discrete microstructures, which is crucial for applications in engineering and materials science. Its ability to maintain accuracy with fewer parameters and provide uncertainty quantification makes it a significant advancement in the field.
Key Takeaways
- GenPANIS allows for bidirectional inference in multiphase media using a unified generative framework.
- The model preserves discrete microstructures while enabling gradient-based methods through continuous latent embeddings.
- It outperforms existing methods with significantly fewer parameters, enhancing efficiency.
- The framework supports training with minimal labeled data and can handle complex boundary conditions.
- Uncertainty quantification is integrated, providing insights into model reliability.
Statistics > Machine Learning arXiv:2602.14642 (stat) [Submitted on 16 Feb 2026] Title:GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media Authors:Matthaios Chatzopoulos, Phaedon-Stelios Koutsourelakis View a PDF of the paper titled GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media, by Matthaios Chatzopoulos and Phaedon-Stelios Koutsourelakis View PDF HTML (experimental) Abstract:Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable and incompatible with gradient-based methods. Existing approaches either relax to continuous approximations, compromising physical fidelity, or employ separate heavyweight models for forward and inverse tasks. We propose GenPANIS, a unified generative framework that preserves exact discrete microstructures while enabling gradient-based inference through continuous latent embeddings. The model learns a joint distribution over microstructures and PDE solutions, supporting bidirectional inference (forward prediction and inverse recovery) within a single architecture. The generative formulation enables training with unlabeled data, physics residuals, and minimal labeled pairs. A physics-aware decoder incorporating a differentiable coarse-grained PDE solver ...
