Multi-fidelity neural network for uncertainty quantification of chemical reaction models

Surrogate models are often used to accelerate the uncertainty quantification (UQ) of chemical kinetic models. However, the construction of surrogate models usually requires the repetitive generation of high-fidelity input-output samples, which is time-consuming. In this work, we utilize a multi-fidelity neural network to speed up the surrogate model construction, yielding a multi-fidelity neural network-based surrogate model (MFNNSM). MFNNSM consists of two separate neural networks. The first neural network learns from high and low-fidelity samples, and then generates samples to train the second neural network for the subsequent UQ analysis. Based on the fact that the uncertainty similarity (sensitivity-based similarity) does exist between the predictions from the reduced and detailed combustion kinetics models, or between the predictions under different conditions, MFNNSM can use reduced model predictions as low-fidelity samples to generate detailed model predictions as the high-fidelity samples, or can transfer samples across different simulations conditions. To demonstrate the MFNNSM method, the ignition delay time (IDT) and laminar flame velocity (LFV) of methanol and n-decane are chosen as model prediction targets for UQ analysis. The results show that MFNNSM can achieve acceleration factors up to 6, by utilizing reduced model samples to generate detailed model samples under the same conditions, and when reusing the reduced model samples under different conditions, the acceleration factor can increase to 10. In addition, the influences of the relative error of the reduced models and the uncertainty similarity coefficients between combustion conditions on the performance of MFNNSM are further discussed, providing the guidance for future applications of MFNNSM.