Extrapolation method of flame nonlinear thermoacoustic response in the time domain based on the kernel embedding of conditional distribution

In this study, we propose a novel method for extrapolating the nonlinear thermoacoustic response of flames in the time domain, based on kernel embedding of conditional distribution (KECD). This approach enables the prediction of full-flame nonlinear responses under high-amplitude oncoming flow disturbances (target domain) using the responses under low-amplitude perturbations (source domain) and a limited dataset of pure-tone flame responses under high-amplitude perturbations. The KECD loss term plays a key role in constraining the neural network to map flame nonlinear responses that are consistent across both the source and target domains. The neural network architecture employed in this work is a Dual-Path model, which integrates two main components: a chronological feature path and a temporal detail feature path, to effectively capture both coarse- and fine-grained temporal features. The proposed method was validated using numerical simulations of a laminar premixed flame. Results demonstrate the method's robust extrapolation performance, achieving an average extrapolation error of approximately 5.1% when the inlet mean flow velocity is 0.6 m/s and 11.1% for a larger inlet flow velocity being 1 m/s.