AI 中文总结
该研究基于直接数值模拟数据库，提出两种不同非线性引入位置的降阶模型，可有效重构、插值和外推瑞利-泰勒不稳定性的动力学，为其演化研究提供了高效建模手段。
AI 中文摘要
我们利用大量直接数值模拟数据库，研究瑞利-泰勒不稳定性向湍流的转变及其向后期自相似区域的演化。除了通过重流体平均浓度剖面追踪混合层的增长外，我们还分析了湍动能和耗散率的一维剖面，这是经典湍流混合模型中的两个关键量。我们考虑两种降阶建模策略，其非线性引入位置不同：要么在隐空间的构建中，要么在其时间演化的描述中。第一种方法使用通过本征正交分解（POD）得到的线性编码器-解码器，其非线性降阶动力学由物理信息神经网络（PINN）学习。第二种方法使用自动编码器学习的非线性编码器-解码器，同时约束隐空间动力学保持线性并满足物理约束。两种方法在瑞利-泰勒不稳定性动力学的重构、插值和外推方面均取得了令人满意的性能。
英文摘要
We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.
