Instabilities in Minimization

From: Sándor Kovács (skovacs_at_wustl.edu)
Date: Tue Jul 17 2012 - 17:14:10 CDT

Greetings experts,

I had a question about the minimization algorithm as implemented in
NAMD.

For a system of ~20,000 atoms, when starting from the same initial
conditions (READ: same atomic positions), the first 5000 steps of my
minimizations are IDENTICAL (as tested with diff).
After this point, however, repeat trials begin to diverge from one-
another, and result in POTENTIAL energies differing by as many as ±10
kcal/mol after 50K minimization steps.
These differences persist when the minimization is carried out for
200K steps (I wanted to make sure each had completely converged).

e.g. for three separate trials after 5000 minimization steps, I obtain
identical results:

[TRIAL 1]
TIMING: 5000 CPU: 184.51, 0.0350367/step Wall: 184.51, 0.0350367/
step, 1.89782 hours remaining, 106.558594 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 5000 1124.8303 4717.7323 3713.3759
139.7911 -34583.7700 -6281.9927 0.0000
0.0000 0.0000 -31170.0331 0.0000
-31170.0331 -31170.0331 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 5000
LINE MINIMIZER BRACKET: DX 0.000499702 0.000999403 DU -0.0921908
0.16983 DUDX -302.606 -66.3689 406.269

[TRIAL 2]
TIMING: 5000 CPU: 184.356, 0.0350742/step Wall: 184.356, 0.0350742/
step, 1.89985 hours remaining, 106.617188 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 5000 1124.8303 4717.7323 3713.3759
139.7911 -34583.7701 -6281.9927 0.0000
0.0000 0.0000 -31170.0331 0.0000
-31170.0331 -31170.0331 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 5000

[TRIAL 3]
TIMING: 5000 CPU: 184.478, 0.035129/step Wall: 184.478, 0.035129/
step, 1.90282 hours remaining, 106.367188 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 5000 1124.8303 4717.7324 3713.3759
139.7911 -34583.7702 -6281.9926 0.0000
0.0000 0.0000 -31170.0331 0.0000
-31170.0331 -31170.0331 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 5000
LINE MINIMIZER BRACKET: DX 0.000499698 0.000999396 DU -0.0921886
0.169841 DUDX -302.606 -66.363 406.287

after 50K minimization steps, one sees a divergence in the tens place:

[TRIAL 1]
LINE MINIMIZER BRACKET: DX 0.000511803 9.74047e-05 DU -0.000141415
5.12214e-06 DUDX -0.552612 3.6656e-08 0.105172
LINE MINIMIZER REDUCING GRADIENT FROM 1.15801 TO 0.00115801
TIMING: 50000 CPU: 1784.96, 0.0353003/step Wall: 1784.96, 0.0353003/
step, 1.47085 hours remaining, 106.535156 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 50000 1129.8369 4769.8503 3772.9891
142.4910 -35065.8099 -6378.5568 0.0000
0.0000 0.0000 -31629.1995 0.0000
-31629.1995 -31629.1995 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 50000

[TRIAL 2]
LINE MINIMIZER BRACKET: DX 0.000580501 0.001161 DU -0.000380669
0.0010312 DUDX -1.1704 -0.141114 1.91753
TIMING: 50000 CPU: 1773.21, 0.0352761/step Wall: 1773.21, 0.0352761/
step, 1.46984 hours remaining, 106.558594 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 50000 1129.6438 4771.2127 3764.2485
140.6916 -35041.1554 -6374.3260 0.0000
0.0000 0.0000 -31609.6847 0.0000
-31609.6847 -31609.6847 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 50000

[TRIAL 3]
LINE MINIMIZER BRACKET: DX 0.000196034 0.000856693 DU -0.00200314
0.0381771 DUDX -20.3922 -0.0399876 89.2622
LINE MINIMIZER REDUCING GRADIENT FROM 123.878 TO 0.123878
TIMING: 50000 CPU: 1836.9, 0.0352672/step Wall: 1836.9, 0.0352672/
step, 1.46947 hours remaining, 107.398438 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 50000 1128.4327 4767.2091 3765.5526
139.9726 -35046.9333 -6368.0236 0.0000
0.0000 0.0000 -31613.7900 0.0000
-31613.7900 -31613.7900 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 50000

and after 200K minimization steps (to ensure convergence to a local
minima), the differences remain:

[TRIAL 1]
LINE MINIMIZER BRACKET: DX 5.58613e-05 0.000330726 DU -2.54659e-11
4.00178e-11 DUDX 2.62465e-08 3.68785e-08 9.98249e-08
TIMING: 200000 CPU: 7113.24, 0.0353183/step Wall: 7113.24, 0.0353183/
step, 0 hours remaining, 107.148438 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 200000 1129.1383 4765.1845 3784.9412
142.4877 -35093.0615 -6379.9375 0.0000
0.0000 0.0000 -31651.2473 0.0000
-31651.2473 -31651.2473 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 200000

[TRIAL 2]
LINE MINIMIZER BRACKET: DX 0.000907904 0.000907904 DU -7.80979e-07
5.97607e-07 DUDX -0.00161935 -0.000100987 0.00141738
TIMING: 200000 CPU: 7119.27, 0.0355447/step Wall: 7119.27, 0.0355447/
step, 0 hours remaining, 107.281250 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 200000 1130.0652 4766.4965 3776.1033
141.0543 -35082.0893 -6370.2935 0.0000
0.0000 0.0000 -31638.6636 0.0000
-31638.6636 -31638.6636 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 200000

[TRIAL 3]
TIMING: 200000 CPU: 7281.36, 0.0350886/step Wall: 7281.36, 0.0350886/
step, 0 hours remaining, 107.398438 MB of memory in use.
ETITLE: TS BOND ANGLE DIHED
IMPRP ELECT VDW BOUNDARY
MISC KINETIC TOTAL TEMP
POTENTIAL TOTAL3 TEMPAVG

ENERGY: 200000 1129.6536 4770.1929 3775.7018
141.1868 -35087.2720 -6374.7239 0.0000
0.0000 0.0000 -31645.2607 0.0000
-31645.2607 -31645.2607 0.0000

WRITING EXTENDED SYSTEM TO RESTART FILE AT STEP 200000

I thought the minimization procedure was deterministic--i.e. repeat
trials should all converge to the same energy minimum (ideally the
global one, but I understand that they can be 'stuck' in local minima).
Is there something going on (stochastic, perhaps) during the
minimization procedure which would account for this discrepancy?

Alternatively, is there a better procedure I should be following If I
would like to obtain an estimate of the system's potential energy for
comparison to similar systems with, say, slightly differently
protonated sites?

I can make input files available off-list if someone needs to
reproduce the above.

Thanks,
Sándor
________________________________________________________
Sándor Ádám Kovács, B.S. M.S.
President, Association of Graduate Engineering Students (AGES)
Ph.D. Candidate and Graduate Research Assistant
Department of Energy, Environmental and Chemical Engineering
Washington University in St. Louis -- St. Louis, MO 63130 -- U.S.A.

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