Non-reproducible PMF Output from Colvars Poisson Integrator

[fhh2626]

Dear Jerome,

test_integrator.zip

I encountered an unexpected discrepancy when using the default Poisson integrator in Colvars. After completing a 200-ns simulation (semi-eABF and the czar.grad files were adopted), I obtained gradient, count, and PMF files (1.grad, 1.count, 1.auto.pmf). Upon restarting the simulation for 10 additional steps, I generated a second set of output files (2.grad, 2.count, 2.auto.pmf).

The gradient files (1.grad vs. 2.grad) show minimal differences (< (10^-5)), as expected. However, the PMF files (1.auto.pmf vs. 2.auto.pmf) exhibit significant deviations.

To investigate potential stability issues in the Poisson integrator, I conducted a control test:

• Performed two fake-ABF simulations integrating 1.grad → generated 1.fake_abf.pmf
• Performed two fake-ABF simulations integrating 2.grad → generated 2.fake_abf.pmf

Results showed:

1. Δ(1.fake_abf.pmf vs. 2.fake_abf.pmf) = negligible
2. Δ(1.fake_abf.pmf vs. 1.auto.pmf) = substantial
3. Δ(2.fake_abf.pmf vs. 2.auto.pmf) = substantial

This suggests potential issues in either:

• Numerical stability of the Poisson integrator, or
• Implementation details affecting PMF reconstruction

I would appreciate your insights on this behavior.

Thank you in advance,
Haohao

[jhenin]

Thank you for the report @fhh2626 ! Let me ask a student who is working on a theoretically more robust version.
@levo-str Can you please have a look at this report?

[jhenin]

@fhh2626 We are unsure what you mean by "fake-ABF simulations". Can you elaborate please?

[fhh2626]

@jhenin Sorry for forgetting to reply. Fake-ABF simulations is using something like

 abf {
   colvars l theta
   inputPrefix  1
}

to generate the pmf file from a grad file.

[fhh2626]

We have implemented an integrator using weight least square method and the result is quite close to the *.auto.pmf. We suspect that there is something weired in fake-ABF simulations.