Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty

2025/11/21 by Xun Zhang, Weijie Yang, Zhang, Xun +5
Computer Science · Earth and Planetary Sciences · Environmental Science · #Advanced Mathematical Modeling in Engineering #FOS: Computer and information sciences #FOS: Physical sciences #Geophysical and Geoelectrical Methods #Geophysics (physics.geo-ph) #Groundwater flow and contamination studies #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.2511.16926

openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/28

Abstract

We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which flexibly incorporates sparse, multi-source observational data, including hydraulic head, solute concentration, and hard conductivity data, through conditional injection mechanisms. These conditioning inputs subsequently guide the generative inversion process during sampling. Bypassing iterative forward simulations, DIN leverages stochastic sampling and probabilistic modeling mechanisms to directly generate ensembles of posterior parameter fields by repeatedly executing the reverse denoising process. Two representative posterior scenarios, Gaussian and non-Gaussian, are investigated. The results demonstrate that DIN can produce multiple constraint-satisfying realizations under identical observational conditions, accurately estimate hydraulic-conductivity fields, and achieve reliable uncertainty quantification. The framework exhibits strong generalization capability across diverse data distributions, offering a robust and unified alternative to conventional multi-stage inversion methodologies.

Citations

• A Fourier Space Perspective on Diffusion Models
• Physics-Informed Convolutional Decoder (PICD): A novel approach for direct inversion of heterogeneous subsurface flow
• Diffusion Models: A Comprehensive Survey of Methods and Applications
• High-Resolution Image Synthesis with Latent Diffusion Models
• Denoising Diffusion Probabilistic Models
• Generative Modeling by Estimating Gradients of the Data Distribution
• Large Scale Structure of Neural Network Loss Landscapes
• FiLM: Visual Reasoning with a General Conditioning Layer
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• A Connection Between Score Matching and Denoising Autoencoders

Related

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• Diffusion models for multivariate subsurface generation and efficient probabilistic inversion
• Physics-Informed Convolutional Decoder (PICD): A novel approach for direct inversion of heterogeneous subsurface flow
• DiffusionInv: Prior-enhanced Bayesian Full Waveform Inversion using Diffusion models
• Combining noisy well data and expert knowledge in a Bayesian calibration of a flow model under uncertainties: an application to solute transport in the Ticino basin