Traditional numerical simulation methods require substantial computational resources to accurately determine the complete nonlinear thermoacoustic response of flames to various perturbation frequencies and amplitudes. In this paper, we have developed deep learning algorithms that can construct a comprehensive flame nonlinear response from limited numerical simulation data. To achieve this, we propose using a frequency-sweeping data type as the training dataset, which incorporates a rich array of learnable information within a constrained dataset. To enhance the precision in learning flame nonlinear response patterns from the training data, we introduce a Dual-Path neural network. This network consists of a Chronological Feature Path and a Temporal Detail Feature Path. The Dual-Path network is specifically designed to focus intensively on the temporal characteristics of velocity perturbation sequences, yielding more accurate flame response patterns and enhanced generalization capabilities. Validations confirm that our approach can accurately model flame nonlinear responses, even under conditions of significant nonlinearity, and exhibits robust generalization capabilities across various test scenarios.

翻译：传统数值模拟方法需要大量计算资源才能准确确定火焰对不同扰动频率和振幅的完整非线性热声响应。本文开发了能够从有限数值模拟数据构建全面火焰非线性响应的深度学习算法。为实现这一目标，我们提出采用扫频数据类型作为训练数据集，该数据类型在有限数据集中包含了丰富的可学习信息。为提升从训练数据中学习火焰非线性响应模式的精度，我们引入了一种双路径神经网络。该网络由时序特征路径与时间细节特征路径构成。双路径网络专门设计用于深度聚焦速度扰动序列的时间特性，从而产生更精确的火焰响应模式并增强泛化能力。验证结果表明，即使在强非线性条件下，我们的方法仍能精确建模火焰非线性响应，并在多种测试场景中展现出稳健的泛化性能。