Potential issue: all methods should do the same autoregressive time progressing

[zongyi-li]

Thanks for putting together this benchmark. This kind of effort is genuinely valuable. I also understand how challenging it is to implement every baseline in a consistent and faithful way. I’m raising the following point because I think it may materially affect accuracy and the fairness of comparisons, and I’d like to help improve the benchmark if possible.

For chaotic systems, how time is modeled can substantially change the task (and the resulting error). In the current implementation, it appears that the FNO baseline treats the temporal dimension as an additional spatial dimension and applies a 2D convolution / 2D FNO over (space × time):
https://github.com/CTF-for-Science/ctf_fno/blob/main/fno.py
This effectively changes the learning problem from predicting new time to predicting the entire trajectory, which is impossible in the chaotic systems.

A more standard approach for forecasting is to apply an FNO over the spatial dimension only, and then progress in time autoregressively. This is the formulation used in the Markov Neural Operator work and reference implementation:
https://github.com/neuraloperator/markov_neural_operator

This is also aligned with how other baselines such as LSTMs and Reservoir Computing treat time (explicit sequential progression rather than folding time into a spatial axis).