Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy

63/2024

Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy

Thursday 12th September 2024

Vitullo, P.; Franco, N.R.; Zunino, P.

Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D multiscale computational model of microcirculation. To this purpose, we present a deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method that integrates the information of a multiscale full-order model (FOM) with that coming from a deep learning enhanced non-intrusive projection-based reduced order model (ROM). The latter is constructed by leveraging on proper orthogonal decomposition (POD) and mesh-informed neural networks (previously developed by the authors and co-workers), integrating diverse architectures that approximate POD coefficients while introducing fine-scale corrections for the microstructures. The DL-MFMC approach provides a robust estimator of specific quantities of interest and their associated uncertainties, with optimal management of computational resources. In particular, the computational budget is efficiently divided between training and sampling, ensuring a reliable estimation process suitably exploiting the ROM speed-up. Here, we apply the DL-MFMC technique to accelerate the estimation of biophysical quantities regarding oxygen transfer and radiotherapy outcomes. Compared to classical Monte Carlo methods, the proposed approach shows remarkable speed-ups and a substantial reduction of the overall computational cost.

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Piermario Vitullo, Nicola Rares Franco, Paolo Zunino. Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy. Foundations of Data Science. doi: 10.3934/fods.2024022