GenAI4UQ: A Software for Inverse Uncertainty Quantification Using Conditional Generative Models

TL;DR

This work tackles the computational bottleneck of inverse uncertainty quantification in scientific modeling by replacing traditional MCMC with a conditional generative framework that learns a direct mapping from observations to parameter distributions. It introduces a score-function approach using a deterministic reverse-time ODE and a training-free mini-batch Monte Carlo estimator to generate labeled data for supervised learning of a fully connected neural network. Key innovations include automated hyperparameter tuning with Ray Tune, extensive overfitting controls, and a modular software architecture that enables automated model development with minimal ML expertise. Demonstrations across bimodal calibration, Earth system model calibration, and high-dimensional pressure-field forecasting show accurate posterior distributions and scalable uncertainty quantification, with practical impact for climate, hydrology, and subsurface applications.

Abstract

We introduce GenAI4UQ, a software package for inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting in scientific applications. GenAI4UQ leverages a generative artificial intelligence (AI) based conditional modeling framework to address the limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of model input parameters and generation of output predictions directly from observations. The software's design allows for rapid ensemble forecasting with robust uncertainty quantification, while maintaining high computational and storage efficiency. GenAI4UQ simplifies the model training process through built-in auto-tuning of hyperparameters, making it accessible to users with varying levels of expertise. Its conditional generative framework ensures versatility, enabling applicability across a wide range of scientific domains. At its core, GenAI4UQ transforms the paradigm of inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling. (The code and data are available at https://github.com/patrickfan/GenAI4UQ).

Figures (9)

• Figure 1: Workflow of the proposed GenAI4UQ conditional generative framework. (a) Initial data preparation, where $X$ represents model parameters or prediction variables, and $Y$ denotes corresponding observations. (b) Labeled data pair generation using the developed Monte Carlo estimator; (c) Supervised training of a fully connected neural network to learn the conditional mapping; (d) Comprehensive model evaluation and uncertainty quantification.
• Figure 2: Flow chart for software architecture and component interactions: it shows the interconnections between different modules and the sequential/parallel processing steps in the GenAI4UQ software pipeline.
• Figure 3: Training performance for the bimodal case. (a) Training and validation loss curves over epochs, demonstrating stable convergence without overfitting. (b) Validation results showing the linear relationship between true and predicted values, with an $R^2$ value close to 1, indicating the model's high accuracy in capturing the data distribution.
• Figure 4: Posterior distribution estimation for input parameter $X$ in the bimodal case, evaluated on four randomly selected test samples. The red lines indicate the true values.
• Figure 5: Training performance for the ELM parameter calibration case. (a) Training and validation loss curves over epochs. (b) Validation results with an $R^2$ analysis.