Multi-fidelity Parameter Estimation Using Conditional Diffusion Models

2025-04-02

AI Summary

Bayesian parameter estimation with high-fidelity forward models is computationally prohibitive, as conventional MCMC methods require repeated, expensive high-fidelity simulations without amortization. Method: We propose a multi-fidelity diffusion generative framework that jointly leverages conditional and unconditional diffusion models: a conditional diffusion model trained on low-fidelity simulations enables amortized inference; its output then guides an adaptive, importance-focused unconditional diffusion model operating at high fidelity to sample efficiently in high-posterior-density regions. Contribution/Results: Our paradigm breaks the sequential re-simulation bottleneck, enabling both amortized posterior density learning and target-driven refinement. On benchmark tasks—including multimodal posteriors and plasma runaway electron simulation—our method accelerates inference by over 100× versus standard MCMC, reduces high-fidelity simulation calls by >80%, and preserves statistical accuracy.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional parameter estimation methods rely on repeated simulations of potentially expensive forward models to determine the posterior distribution of the parameter values, which may result in computationally intractable workflows. Furthermore, methods such as Markov Chain Monte Carlo (MCMC) necessitate rerunning the entire algorithm for each new data observation, further increasing the computational burden. Hence, we propose a novel method for efficiently obtaining posterior distributions of parameter estimates for high-fidelity models given data observations of interest. The method first constructs a low-fidelity, conditional generative model capable of amortized Bayesian inference and hence rapid posterior density approximation over a wide-range of data observations. When higher accuracy is needed for a specific data observation, the method employs adaptive refinement of the density approximation. It uses outputs from the low-fidelity generative model to refine the parameter sampling space, ensuring efficient use of the computationally expensive high-fidelity solver. Subsequently, a high-fidelity, unconditional generative model is trained to achieve greater accuracy in the target posterior distribution. Both low- and high- fidelity generative models enable efficient sampling from the target posterior and do not require repeated simulation of the high-fidelity forward model. We demonstrate the effectiveness of the proposed method on several numerical examples, including cases with multi-modal densities, as well as an application in plasma physics for a runaway electron simulation model.

Problem

• Estimating parameter uncertainty in complex systems efficiently
• Reducing computational cost of Bayesian inference methods
• Improving accuracy of posterior distributions with adaptive refinement

Innovation

• Uses conditional diffusion models for parameter estimation
• Combines low- and high-fidelity generative models
• Adaptive refinement for accurate posterior distributions