Question about Chapter 19: e3nn on trajectory prediction

[jipq6175]

Hello, thank you so much for the book and tutorials.
I have a question re: ch.19 (./applied/e3nn_traj.ipynb).

The baseline model was trained to predict the coordinates of the next time frame $x(t+1)$ but the equivariant model was trained to predict the distance vector, $dx(t) = x(t+1) - x(t)$. It might not be a fair comparison.. since $P(x(t+1) | x(t))$ differs from $P(dx(t) | x(t))$ and the later might be easier to approximate?

I further tried using a simple MLP (of course not equivariant) for distance vector prediction and the performance was on par with the equivariant model, in terms of center of mass and individual particle coordinate.

MLP prediction vs truth:

MLP trajectory comparison on the test set

Additionally, the e3nn model had reduced performance when trained to predict $x(t+1)$.

Say, if one only has data to perform position prediction, with data available at $x(t)$ and $x(t+T)$ where $T$ is a large time interval, it might still be challenging for e3nn to predict $P(x(t+T) | x(t))$..?

I wonder what your thoughts are on this?

Thanks a lot!

[whitead]

Can you take a look @SamCox822? She would know better than me on this.