一种TVD神经网络封闭及其在湍流燃烧中的应用
A TVD neural network closure and application to turbulent combustion
AI总结：
本文提出受TVD方法严格约束的神经网络封闭模型，通过参数重缩放保证解的有界性与非振荡性，并成功用于湍流反应流SGS建模。
摘要：
经过训练的神经网络（NN）在封闭控制方程方面具有吸引人的特性。许多方法正展现出前景，但当小误差随之违反物理现实（例如解的有界性条件）时，所有方法都可能失效。本文引入一种NN公式，以防止违反解的有界性或正性的虚假振荡。它作为机器学习封闭项嵌入离散方程中，并受到严格约束，其灵感来自双曲守恒律的总变差递减（TVD）方法。该约束在梯度下降训练期间通过重新缩放NN参数而被精确施加，从而将参数映射到一个显式可行集上。演示表明，受约束的NN封闭模型在保持非振荡特性的同时，有效恢复了线性和非线性双曲现象以及反扩散。最后，该模型被应用于湍流反应流的亚格子尺度（SGS）建模，在此任务中它抑制了标量场中原本会违反解有界性的虚假振荡。其表现优于在损失函数中对振荡进行简单惩罚的方法。
英文摘要：
Trained neural networks (NN) have attractive features for closing governing equations. There are many methods that are showing promise, but all can fail in cases when small errors consequentially violate physical reality, such as a solution boundedness condition. A NN formulation is introduced to preclude spurious oscillations that violate solution boundedness or positivity. It is embedded in the discretized equations as a machine learning closure and strictly constrained, inspired by total variation diminishing (TVD) methods for hyperbolic conservation laws. The constraint is exactly enforced during gradient-descent training by rescaling the NN parameters, which maps them onto an explicit feasible set. Demonstrations show that the constrained NN closure model usefully recovers linear and nonlinear hyperbolic phenomena and anti-diffusion while enforcing the non-oscillatory property. Finally, the model is applied to subgrid-scale (SGS) modeling of a turbulent reacting flow, for which it suppresses spurious oscillations in scalar fields that otherwise violate the solution boundedness. It outperforms a simple penalization of oscillations in the loss function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
