GenUQ: Predictive Uncertainty Estimates via Generative Hyper-Networks

2025-09-25

AI Summary

This paper addresses the challenge of uncertainty quantification (UQ) in operator learning, where explicit likelihood functions are often intractable. We propose GenUQ, a measure-theoretic generative UQ framework that bypasses likelihood modeling entirely. Instead, GenUQ employs a generative hypernetwork to directly learn the posterior distribution over parameters from observational data, enabling robust UQ for complex functional mappings—such as those arising in stochastic partial differential equations (PDEs). By tightly integrating operator learning, generative modeling, and hypernetwork architecture, GenUQ achieves likelihood-free, end-to-end trainability and high-fidelity posterior sampling. Experiments demonstrate that GenUQ significantly outperforms existing UQ methods on diverse tasks—including manufacturing operator reconstruction, stochastic elliptic PDE solving, and porous steel tensile failure localization—yielding improved predictive reliability and enhanced physical consistency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Operator learning is a recently developed generalization of regression to mappings between functions. It promises to drastically reduce expensive numerical integration of PDEs to fast evaluations of mappings between functional states of a system, i.e., surrogate and reduced-order modeling. Operator learning has already found applications in several areas such as modeling sea ice, combustion, and atmospheric physics. Recent approaches towards integrating uncertainty quantification into the operator models have relied on likelihood based methods to infer parameter distributions from noisy data. However, stochastic operators may yield actions from which a likelihood is difficult or impossible to construct. In this paper, we introduce, GenUQ, a measure-theoretic approach to UQ that avoids constructing a likelihood by introducing a generative hyper-network model that produces parameter distributions consistent with observed data. We demonstrate that GenUQ outperforms other UQ methods in three example problems, recovering a manufactured operator, learning the solution operator to a stochastic elliptic PDE, and modeling the failure location of porous steel under tension.

Problem

• Generating predictive uncertainty estimates without likelihood construction
• Developing generative hyper-networks for operator learning UQ
• Solving stochastic operator problems with data-consistent parameter distributions

Innovation

• Generative hyper-network model for uncertainty quantification
• Likelihood-free approach using measure-theoretic framework
• Produces parameter distributions consistent with observed data