Uncertainties pervade scientific data, stemming from various sources such as measurement errors, noise, or incomplete information. Overcoming these uncertainties is important for creating reliable model-based predictions and inferences, providing deeper insights into the mathematical models and the physical systems they represent. Therefore, uncertainty quantification (UQ) is essential for robust decision-making in scientific modelling, particularly in fields characterised by complex, large-scale systems. Bayesian inference offers a framework for quantifying uncertainties, yet its application to large-scale simulation models remains limited due to computational and algorithmic challenges. Parallelized Multi-index Delayed Acceptance (MIDA) extends the capabilities of Bayesian inference by leveraging a multi-index hierarchy of models and significantly reduces the computational burden associated with traditional Markov chain Monte Carlo (MCMC) methods, enabling inference on extreme-scale models while preserving unbiased results. In this innovation study, MIDA is integrated with UM-Bridge, a universal software interface, facilitating seamless communication between uncertainty quantification algorithms and simulation software. This integration not only enhances the efficiency of large-scale simulations but also enables broader applicability across diverse fields. Through this study, the efficacy of advancing inference under uncertainty for realistic models is demonstrated.

MIDA builds upon the principles of Multilevel Delayed Acceptance (MLDA), a Markov chain Monte Carlo (MCMC) algorithm, to efficiently explore the Bayesian posterior distribution. By operating on a multi-index hierarchy of models, MIDA reduces the number and size of forward simulations required for inference, thus mitigating the computational overhead associated with traditional MCMC methods. Furthermore, MIDA incorporates a novel approach to parallelising hierarchical UQ methods, thereby enabling its scalability to exascale supercomputers. The integration of MIDA with UM-Bridge, a universal software interface, facilitates seamless communication between uncertainty quantification algorithms and simulation software, enabling efficient coupling of advanced UQ methods with modern simulation models. This study demonstrates the applicability of ScalaMIDA in earthquake physics and ground shaking studies, showcasing its ability to yield unbiased results while significantly reducing computational costs.

The development of MIDA represents a significant advancement in the field of uncertainty quantification for large-scale simulation models. MIDA provides a scalable solution for addressing uncertainties in complex systems. The integration with UM-Bridge enhances the usability and accessibility of the algorithm. This study exemplifies the transformative potential of advancing scientific understanding and decision-making in complex systems.