Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling
This method addresses parameterized problems in computational modeling by enabling efficient simulations without intrusive modifications, though it appears incremental as it builds on existing reduced basis and neural network techniques.
The paper tackles the problem of nonintrusive reduced-order modeling by proposing a method that uses proper orthogonal decomposition and a shallow neural network to learn high-fidelity reduced coefficients from low-fidelity data, achieving improved predictive capability and decoupling high-fidelity simulations from online stages.
In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to other methods, one distinct feature of the proposed method is to incorporate the features extracted from the low-fidelity data as the input feature, this approach not only improves the predictive capability of the neural network but also enables the decoupling the high-fidelity simulation from the online stage. Due to its nonintrusive nature, it is applicable to general parameterized problems. We also provide several numerical examples to illustrate the effectiveness and performance of the proposed method.