论文标题
学习过滤的离散操作员：非侵入性与侵入性方法
Learning filtered discretization operators: non-intrusive versus intrusive approaches
论文作者
论文摘要
模拟多尺度现象（例如湍流流量）通常在计算上非常昂贵。过滤较小的尺度可以使用粗离散化，但是，这需要闭合模型来解释未解决的对解决量表的影响。常见的方法是过滤连续方程，但由于非线性项，不均匀过滤器或边界条件，这会导致几个换向器错误。 我们提出了一种新的过滤方法，该方法首先离散，然后进行过滤。对于应用于线性对流方程的不均匀过滤器，我们表明可以使用三种方法推断出离散过滤的对流操作员：通过“衍生拟合拟合”或“轨迹拟合”或“轨迹拟合”（嵌入式学习），可以通过侵入性（显式重建）或非侵入性操作员推理（嵌入式学习）。我们表明，明确的重建和衍生拟合拟合确定了类似的操作员并产生小错误，但是这种轨迹拟合需要巨大的努力才能训练以实现相似的性能。但是，明确的重建方法更容易不稳定。
Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the effects of the unresolved on the resolved scales. The common approach is to filter the continuous equations, but this gives rise to several commutator errors due to nonlinear terms, non-uniform filters, or boundary conditions. We propose a new approach to filtering, where the equations are discretized first and then filtered. For a non-uniform filter applied to the linear convection equation, we show that the discretely filtered convection operator can be inferred using three methods: intrusive (`explicit reconstruction') or non-intrusive operator inference, either via `derivative fitting' or `trajectory fitting' (embedded learning). We show that explicit reconstruction and derivative fitting identify a similar operator and produce small errors, but that trajectory fitting requires significant effort to train to achieve similar performance. However, the explicit reconstruction approach is more prone to instabilities.
