Hello folks, thanks for the wonderful work. I wanted to ask a couple of questions to clarify myself of the functionality of the framework

1. The way i understand this, resolution invariance helps in making predictions at difference resolutions eventhough training is on a lower/higher resolution. I was wondering if it makes sense/even possitble to train the network to have input channels of shape 256x256 and make the predictions on 64x64? does this help in learning the boundaries conditions better?

2. From initial experiments, I noticed that if we trained the model using n- timestamps for input, during inference as well, it's important to use n timestamps eventhough it's flexible to change the resolution, is this a feature or it's possible to make the number of timesteps varying during inference time both for inputs and outputs?

3. I used the FNO2d class to train on the navier_stokes_2d_with_time dataset. The predictions of the model given an input(T+0, from dataset) to only predict the next immediate output (T+1, from dataset) works decent however, using the model predictions autoregressively to make predictions of higher timestamps T+2, T+3 etc gets unstable pretty quickly. In some discussions, I noticed that one could train using FNO3d as well instead, could this help in making better predictions for higher timestamps as multiple timesteps are already part of an output?

Clarification regarding this would be greatly appreciated, Thank you!