论文标题
学会解决图形网络的PDE构成的逆问题
Learning to Solve PDE-constrained Inverse Problems with Graph Networks
论文作者
论文摘要
最近已经建立了学到的图形神经网络（GNN），作为在模拟物理系统动力学方面的原则求解器的快速准确替代方案。但是，在科学和工程跨越的许多应用领域中，我们不仅对远期模拟感兴趣，而且对解决由部分微分方程（PDE）定义的约束的逆问题感兴趣。在这里，我们探索GNN来解决此类PDE构成的反问题。给定一组稀疏的测量值，我们有兴趣恢复PDE的初始条件或参数。我们证明，与AutoDecoder风格的先验相结合的GNN非常适合这些任务，比应用于Wave方程或Navier-Stokes方程时，比其他学到的方法更准确地估计了初始条件或物理参数。与原则上的求解器相比，我们还使用GNN证明了高达90倍的计算加速度。项目页面：https：//cyanzhao42.github.io/learninverseproblem
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering, however, we are not only interested in a forward simulation but also in solving inverse problems with constraints defined by a partial differential equation (PDE). Here we explore GNNs to solve such PDE-constrained inverse problems. Given a sparse set of measurements, we are interested in recovering the initial condition or parameters of the PDE. We demonstrate that GNNs combined with autodecoder-style priors are well-suited for these tasks, achieving more accurate estimates of initial conditions or physical parameters than other learned approaches when applied to the wave equation or Navier-Stokes equations. We also demonstrate computational speedups of up to 90x using GNNs compared to principled solvers. Project page: https://cyanzhao42.github.io/LearnInverseProblem
