论文标题
求解器中的求解器：从可区分的物理学中学习以与迭代PDE-SOLVERS相互作用
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
论文作者
论文摘要
在所有科学和工程学科中，找到针对部分微分方程（PDE）的准确解决方案是至关重要的任务。最近已经证明，机器学习方法可以通过校正离散的PDE捕获的效果来提高解决方案的准确性。我们针对减少迭代PDE求解器的数值误差的问题，并比较寻找复杂校正功能的不同学习方法。我们发现，以前使用的学习方法的表现明显优于将求解器集成到训练环中，从而使模型在训练过程中与PDE相互作用。这为模型提供了现实的输入分布，这些分布将考虑到以前的更正，从而通过数百个经常性评估步骤进行稳定的推出，并超越了量身定制的监督变体，从而可以提高准确性。我们强调了各种PDE的可区分物理网络的性能，从非线性的对流扩散系统到三维Navier-Stokes Flow。
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.
