A DeepONet multi-fidelity approach for residual learning in reduced order modeling
This work addresses the trade-off between speed and accuracy in reduced order modeling for computational simulations, offering an incremental improvement by integrating existing techniques.
The authors tackled the error in reduced order models by proposing a multi-fidelity approach that uses DeepONets for residual learning, achieving enhanced precision in numerical approximations for parametric problems like a Navier-Stokes benchmark.
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.