A DeepONet multi-fidelity approach for residual learning in reduced order modeling

In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

Automated summary

In this work, a novel approach is introduced to enhance the precision of reduced order models by utilizing a multi-fidelity perspective and DeepONets. The integration of model reduction with machine learning residual learning allows the neural network to learn and infer the error introduced by the simplification operation. The exploitation of high-fidelity information for building the reduced order model and learning the residual is emphasized in the framework.