GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media

• URL: http://arxiv.org/abs/2602.14642v1
• Date: Mon, 16 Feb 2026 11:08:30 GMT
• Title: GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media
• Authors: Matthaios Chatzopoulos, Phaedon-Stelios Koutsourelakis,
• Abstract summary: Inverse problems and inverse design in multiphase media require operating on discrete-valued material fields.<n>We propose GenPANIS, a unified generative framework that preserves exact discrete microstructures.<n>A physics-aware decoder incorporating a differentiable coarse-grained PDE solver preserves governing equation structure.
• Score: 0.8594140167290095
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 preserves governing equation structure, enabling extrapolation to varying boundary conditions and microstructural statistics. A learnable normalizing flow prior captures complex posterior structure for inverse problems. Demonstrated on Darcy flow and Helmholtz equations, GenPANIS maintains accuracy on challenging extrapolative scenarios - including unseen boundary conditions, volume fractions, and microstructural morphologies, with sparse, noisy observations. It outperforms state-of-the-art methods while using 10 - 100 times fewer parameters and providing principled uncertainty quantification.

Related papers

• Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI [1.6863755729554886]
  We present Spinverse, a permeability-aware reconstruction method that inverts dMRI measurements.<n>Spinverse represents tissue on a fixed tetrahedral grid and treats each interior face permeability as a learnable parameter.<n>It reconstructs diverse geometries and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions.
  arXiv  Detail & Related papers  (2026-03-04T21:57:40Z)
• Riemannian Flow Matching for Disentangled Graph Domain Adaptation [51.98961391065951]
  Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space.<n>DisRFM is a geometry-aware GDA framework that unifies embedding and flow-based transport.
  arXiv  Detail & Related papers  (2026-01-31T11:05:35Z)
• Soft Partition-based KAPI-ELM for Multi-Scale PDEs [0.0]
  This work introduces a soft partition-based Kernel-Adaptive Physics-Informed Extreme Learning Machine.<n>A signed-distance-based weighting stabilizes least-squares learning on irregular frequencies.<n>Although demonstrated on steady linear PDEs, the results show that soft-partition kernel adaptation provides a fast, architecture-free approach for multiscale PDEs.
  arXiv  Detail & Related papers  (2026-01-13T16:43:38Z)
• CompNO: A Novel Foundation Model approach for solving Partial Differential Equations [0.0]
  Partial differential equations govern a wide range of physical phenomena, but their numerical solution remains computationally demanding.<n>Recent Scientific Foundation Models (SFMs) aim to alleviate this cost by learning universal surrogates from large collections of simulated systems.<n>We introduce Compositional Neural Operators (CompNO), a compositional neural operator framework for parametric PDEs.
  arXiv  Detail & Related papers  (2026-01-12T10:04:48Z)
• Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching [60.37045080890305]
  We provide the first analysis of the sample complexity for flow-matching based generative models.<n>We decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field.
  arXiv  Detail & Related papers  (2025-12-01T05:14:25Z)
• Riemannian Consistency Model [57.933800575074535]
  We propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling.<n>We derive the closed-form solutions for both discrete- and continuous-time training objectives for RCM.<n>We provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles.
  arXiv  Detail & Related papers  (2025-10-01T14:57:25Z)
• Cryo-EM as a Stochastic Inverse Problem [3.7068356204071637]
  Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules.<n>Traditional methods assume a discrete set of conformations, limiting their ability to recover continuous structural variability.<n>We formulate cryo-EM reconstruction as an inverse problem (SIP) over probability measures.<n>We numerically solve using particles to represent and evolve conformational ensembles.
  arXiv  Detail & Related papers  (2025-09-05T23:35:04Z)
• Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models [50.90868087591973]
  We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation.
  arXiv  Detail & Related papers  (2024-08-20T19:06:02Z)
• Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics [11.919291977879801]
  Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Diffusion models have shown promise as potent generative tools for solving inverse problems.
  arXiv  Detail & Related papers  (2024-06-19T15:55:12Z)
• Fully probabilistic deep models for forward and inverse problems in parametric PDEs [1.9599274203282304]
  We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to- parameter (inverse) maps of PDEs. The proposed framework can be easily extended to seamlessly integrate observed data to solve inverse problems and to build generative models. We demonstrate the efficiency and robustness of our method on finite element discretized parametric PDE problems.
  arXiv  Detail & Related papers  (2022-08-09T15:40:53Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.