A multi-fidelity transfer learning strategy based on multi-channel fusion

Multi-fidelity strategies leverage a large amount of low-fidelity data combined with a smaller set of high-fidelity data, thereby achieving satisfactory results at a reasonable cost. In our research, we introduce an innovative multi-fidelity strategy that integrates the concepts of multi-fidelity data fusion and transfer learning. In the proposed framework, we incorporate auto-encoders and a multi-channel transfer learning strategy, enabling the network model to comprehend the relationship between the low-fidelity and high-fidelity models in both explicit and implicit manners. This approach not only enhances prediction accuracy but also mitigates issues such as overfitting and negative transfer, which may arise in scenarios with sparse samples. Additionally, Bayesian optimization is employed for effective hyperparameter selection. To evaluate and analyze the performance of our proposed method, we present a series of benchmark test cases. Furthermore, we also show the application of the proposed method to engineering problems. Firstly, we consider a parametrized partial differential equation problem, where high-fidelity and low-fidelity data are obtained using exact methods and simplified algorithms, respectively. Subsequently, we extend this strategy to convolutional neural network architectures, specifically addressing a pressure Poisson equation problem. We also explore the effect of the reliability of the low-fidelity data and the number of high-fidelity data on the results. The results show that the proposed method exhibits low requirements in terms of both the reliability of the low-fidelity data and the number of high-fidelity data while maintaining satisfactory accuracy metrics.