Physics-aware learning of nonlinear limit cycles and adjoint limit cycles

Physics-aware learning of nonlinear limit cycles and adjoint limit cycles
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非线性极限环和伴随极限环的物理感知学习

DOI：
10.3397/in_2022_0163
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发表时间：
2023
期刊：
INTER-NOISE and NOISE-CON Congress and Conference Proceedings
影响因子：
--
通讯作者：
L. Magri
L. Magri
中科院分区：
--
文献类型：
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作者：
D. E. Ozan;L. Magri

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当火焰释放的热量与声压充分同相时，就会发生热声振荡。在这种情况下，线性不稳定性会饱和到大幅度的非线性自激振荡。典型的非线性状态是极限环， 其特征是热声动力学中的周期性轨道。在本文中，我们开发了一种物理感知数据驱动方法，使用前向神经网络预测周期解。物理学受到两个方面的限制。首先，训练由身体残差告知， 它惩罚违反质量、动量和能量守恒定律的解决方案。其次，通过在神经网络中引入周期性激活函数来强加周期性。我们在 Rijke 管的非线性时滞模型上测试了该算法。伴随方法提供了一种廉价且 计算设计参数梯度的简单方法，因此我们将研究扩展到学习 Rijke 系统的伴随变量，这些变量也解决了周期性振荡。我们发现（i）热声系统的周期解可以通过以下方法准确学习 这种方法，（ii）对于周期性数据，周期性激活在超出训练范围的预测能力方面优于传统激活，并且（iii）在物理约束下，更少的数据足以实现良好的性能。这项工作开辟了可能性 通过结合物理知识和数据来预测非线性热声学。
Thermoacoustic oscillations occur when the heat released by a flame is sufficiently in phase with the acoustic pressure. Under this condition, the linear instability can saturate to a nonlinear self-excited oscillation with a large amplitude. A typical nonlinear regime is a limit cycle, which is characterised by a periodic orbit in the thermoacoustic dynamics. In this paper, we develop a physics-aware data-driven method to predict periodic solutions using forward neural networks. The physics is constrained in two ways. First, the training is informed by a physical residual, which penalises solutions that violate the conservation of mass, momentum, and energy. Second, periodicity is imposed by introducing periodic activation functions in the neural network. We test the algorithm on a nonlinear time-delayed model of a Rijke tube. Adjoint methods offer a cheap and easy way to calculate the gradients with respect to design parameters, hence we extend our study to learning the adjoint variables of the Rijke system, which also settle onto periodic oscillations. We find that (i) periodic solutions of thermoacoustic systems can be accurately learned with this method, (ii) for periodic data, periodic activations outperform conventional activations in terms of prediction capability beyond the training range, and (iii) under the physical constraints, fewer data is sufficient to achieve a good performance. This work opens up possibilities for the prediction of nonlinear thermoacoustics by combining physical knowledge and data.