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This paper introduces a bifidelity method for parameter estimation in complex systems that combines low-fidelity and high-fidelity generative models to efficiently approximate Bayesian posterior distributions. The approach first uses a computationally cheap conditional generative model for rapid inference across many data observations, then refines estimates for specific cases using a high-fidelity unconditional generative model trained on a reduced parameter space. This eliminates the need for repeated expensive simulations required by traditional methods like Markov Chain Monte Carlo, while maintaining accuracy through adaptive refinement.
Why it matters
This method could significantly reduce computational costs in fields requiring repeated parameter estimation from observational data, such as climate modeling, medical imaging, and plasma physics. By enabling amortized inference that doesn't require rerunning algorithms for each new observation, it makes Bayesian uncertainty quantification practical for expensive simulation models that were previously computationally intractable.
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arXiv:2504.01894v2 Announce Type: replace
Abstract: We present a bifidelity 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.
Source: Bifidelity Parameter Estimation Using Conditional Diffusion Models