How to train dynamical PDE system in PINO?

In the example documentation of PINO, it uses stationary PDE(input tensor shape: 1024,1,421,421). But my PDE depends on time, so my input tensor shape is (1024,100,421,421).
Can you kindly guide me how to solve dynamical PDE in PINO?

Hi @id21resch11019

We presently do not have an example of PINO for a transient problem, just 2D steady state. You could predict all time-steps at once with a 4D output and approximate time derivatives using finite difference, Fourier derivatives, etc. in that dimension.

One approach I would consider is an auto-regressive approach which can work well for physical systems with physics based loss functions. For data-driven this is how models like FourCastNet (Adaptive FNO under the hood) operate.