Learning to Trust AI and Data-driven models in Data Assimilation through a Multifidelity Ensemble Gaussian Mixture Filter Framework

2026-04-24

AI Summary

This work addresses the issue of non-physical “hallucinations” in data-driven models within data assimilation, which compromise long-term reliability. To mitigate this, the authors propose a multi-fidelity ensemble Gaussian mixture particle filter that integrates theory-driven and data-driven models through an adaptive trust mechanism. Model credibility is quantified via a bandwidth scaling factor derived from kernel density estimation, which is dynamically optimized using the expectation–maximization algorithm. The framework demonstrates stable convergence even under high-dimensional, undersampled conditions. Its efficacy is validated on both a static banana-shaped distribution problem and the Lorenz '96 dynamical system, significantly enhancing the physical consistency and robustness of data assimilation outcomes.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious question about their long-term use, and can be categorized as untrustworthy methods. Theory-driven methods on the other hand are slow, but are capable of staying physically realistic due to their mathematical underpinning, and can be categorized as trustworthy methods. We argue that by making use of these methods in tandem, it is possible to build a relative measure of trust between the theory-driven and data-driven methods that results in a combined trustworthy methodology. We argue, and then show, that the bandwidth scaling factors in the kernel density estimates can be used to represent our trust in the theory-driven and data-driven models. We provide for ways in which these measures of trust can be adaptively computed through an expectation-maximization approach. We combine all of these ideas to create the multifidelity ensemble Gaussian mixture filter and its adaptive trust version, which are particle filters capable of high-dimensional data assimilation. We validate our ideas on both a static banana problem and on a sequential filtering example with the Lorenz '96 equations, showing that it is possible to create a particle filter that is capable of high dimensional convergent inference in the undersampled regime -- when the number of theory-driven samples is less than the dimension of the system.

Problem

• data assimilation
• trustworthiness
• AI hallucination
• theory-driven models
• data-driven models

Innovation

• multifidelity filtering
• trust calibration
• Gaussian mixture filter
• data assimilation
• expectation-maximization