标量双曲守恒律的基于动力学缺陷测度的结构信息数据驱动降阶建模

中文摘要 AI 辅助

输运主导系统的降阶建模仍然具有挑战性，因为移动的前沿和激波在低维线性子空间中难以得到良好表示。我们基于动力学缺陷公式，为标量双曲守恒律开发了一种结构信息数据驱动的降阶模型（ROM）。该公式将非线性动力学分解为已知的特征输运和局域在激波流形上的动力学熵缺陷。我们利用这一结构，首先从解快照中移除已知的输运部分。然后，我们在激波附着坐标系中提取并配准剩余的缺陷驱动动力学。使用单独的ROM来演化激波几何和配准后的缺陷驱动源。在预测过程中，预测的激波几何用于逆配准学习到的缺陷驱动源，从而推进动力学状态并恢复物理解。一维和二维空间中的数值算例表明，该方法能够准确重建和预测带激波的非线性输运，包括训练区间之外的演化，同时准确捕捉参考解的质量和熵耗散行为。

英文摘要

Reduced-order modeling of transport-dominated systems remains challenging because moving fronts and shocks are poorly represented by low-dimensional linear subspaces. We develop a structure-informed data-driven reduced-order model(ROM) for scalar hyperbolic conservation laws based on the kinetic defect formulation. This formulation separates the nonlinear dynamics into known characteristic transport and a kinetic entropy defect localized on the shock manifold. We exploit this structure by first removing the known transport from the solution snapshots. We then extract and register the remaining defect-driven dynamics in a shock-attached coordinate system. Separate ROMs are used to evolve the shock geometry and the registered defect-driven source. During prediction, the predicted shock geometry is used to inverse-register the learned defect-driven source, which advances the kinetic state and recovers the physical solution. Numerical examples in one and two spatial dimensions demonstrate accurate reconstruction and prediction of nonlinear transport with shocks, including evolution beyond the training interval, while accurately capturing the mass and entropy-dissipation behavior of the reference solution.

发表机构

• Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）
• Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与应用力学系）

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