Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

提出了一种新的数据驱动方法DINo来模拟PDE流场，通过Implicit Neural Representations在小的潜空间中独立嵌入空间观测数据，在由学习ODE驱动的时间中灵活处理时间和空间。DINo可以在任意时间和空间位置外推，并且可以从稀疏的不规则网格或流形中学习，在测试时，可以推广到新的网格或分辨率。该方法在代表性PDE系统上的各种极具挑战的泛化场景中优于替代的神经PDE预测模型。

使用隐式神经表示预测连续偏微分方程动态