help with understanding how the coordinates are updated

[tarak77]

Hi @lh3 ,
I am having a little trouble understanding how the coordinates in hickit code are updated?
I know that in nuclear_dynamics, the change in position is velocitytime + 0.5acceleration*time^2. The calculation of the acceleration is force/mass with an extra term.

Is hickit using similar equation? Also, while going over the code I did not understand the const max_f and coef_moment?

Any help will be great!

[tanlongzhi]

Hi @tarak77,

As far as I understand (@lh3 please correct me if I got it wrong), hickit does not directly model Newtonian dynamics (e.g. 2nd order differential equation) as in nuc_dynamics; however, hickit's use of momentum (controlled by coef_moment) makes the two similar. Please see the code fdg.c for details.

In particular, in the main function hk_fdg1(), the "force" matrix f[][] stores the repulsive and attractive forces via update_force() as in nuc_dynamics. However, this "force" is not used exactly in the same way as acceleration in Newtonian dynamics particle coordinates. In particular:

Hickit first calculates the root-mean-square (RMS) "force" t from f[][] with fv3_L2() and sqrtf(). The RMS value is displayed as RMS_force in standard error, and will be normalized down to max_f (together with the entire f[][]) if it exceeds max_f. Note that hickit does not add random/thermal fluctuation (or calculate RMS velocity to determine temperature) as in nuc_dynamics.

Hickit then updates particle coordinates x[][] using f[][] as a "velocity", by incrementing x[i][j] with f[i][j] * step. However, hickit also retains a memory of the previous update inx[][] - x0[][], and uses it to adjust the current update as a "momentum" (opt->coef_moment * (t - x0[i][j])), making it similar to Newtonian dynamics. The parameter coef_moment controls the contribution of this momentum term (again, @lh3 please correct me if I got it wrong).

Edit: the above has been updated regarding momentum.

Best,
Tan

[lh3]

hickit poses this as an optimization problem. Force is proportional to gradient. We can use gradient descent to find the optima. In the code, hickit is using gradient descent with a momentum term as is often used in deep learning.

Different formulations lead to largely the same result. They differ in convergence time and in the robustness to local optima.

[tanlongzhi]

Thanks a lot @lh3 for the explanation! Under a gradient descent framework, everything makes much more sense now.

@tarak77, we built the whole fdg.c (short for "force-directed graph") to see how much we can simplify nuc_dynamics's energy minimization (i.e. optimization) procedure.

From hickit's results, the use of random/thermal fluctuations turns out not essential; however, hierarchical optimization from coarse to fine bin sizes turns out useful.

Edit: hickit does use gradient descent with momentum (similar to velocity in Newtonian dynamics). I've also edited my previous reply for more details.

Best,
Tan

[tarak77]

I understand now. Thank you!