Potential time-index mismatch in physics integration update (`q_{t+3}` uses `\ddot{q}` at `t+1`)

[pluviophile-psv]

Hi authors, thank you for releasing this great work and codebase.
I have a question about the physics integration step in models/PhysMoP.py:

PhysMoP/models/PhysMoP.py

Line 188 in 61c9158

motion_pred_physics_pred[:, t+3] = 2*motion_pred_physics_pred[:, t+2] - motion_pred_physics_pred[:, t+1] + pred_q_ddot_physics_pred[:, t+1].clone() * constants.dt**2

According to the Verlet/central-difference scheme ( $q_{k+1} = 2q_k - q_{k-1} + \ddot{q_k} \Delta t^2$ ), the acceleration for $q_{t+3}$ should typically be indexed at $t+2$ instead of $t+1$.
Could you clarify this for me? Thanks!

[zhangy76]

Thanks for the reaching out! we did not use central difference but forward difference. They are different in the way to compute velocity or acceleration but the results should be very similar in this task.