[CP2K-user] geometry optimization takes very long time to calculate the Hessian
Nicholas Winner
nwi... at berkeley.edu
Sat May 16 00:51:30 UTC 2020
The Hessian is very expensive to calculate. You can avoid calculating the
Hessian by using CG method, which is based on the gradient without the
hessian. *However,* this is not recommended. Quasi-Netwonian methods like
BFGS that use the Hessian converge very fast once you are near the minimum.
If you choose not to do the BFGS, your individual steps might be faster,
but its possible that it will be slower overall convergence. Since HFX
calculations should always be initialized from a pre-converged GGA
calculation, it is most likely close to the minimum already and just needs
refinement. So BFGS makes sense. Its just the cost of doing business with
hybrid calculations.
One question I have for you, why did you not use ADMM? It trades a small
loss of accuracy for an immense speedup. Personally, I have seen 1000 fold
improvement in calculation speed when using ADMM for some systems.
On Tuesday, September 3, 2019 at 12:17:17 PM UTC-7, Xiaoming Wang wrote:
>
> Hello,
>
> I am trying to do geo_opt with hybrid functionals and MOLOPT basis. I
> didn't use ADMM.
> I know the calculation without ADMM would be very expensive. But it turned
> out that only
> the first OT step took a longer time, the following steps are relatively
> cheap. However,
> between every two ionic steps, it seems to take very long time to
> calculate the Hessian.
> Is this expected for the current condition? And is there any way to reduce
> the time?
>
>
> Here is part of the output:
>
> OPTIMIZATION STEP: 3
> --------------------------
>
> Spin 1
>
> Number of electrons:
> 865
> Number of occupied orbitals:
> 865
> Number of molecular orbitals:
> 865
>
> Spin 2
>
> Number of electrons:
> 863
> Number of occupied orbitals:
> 863
> Number of molecular orbitals:
> 863
>
> Number of orbital functions:
> 2916
> Number of independent orbital functions:
> 2916
>
> Parameters for the always stable predictor-corrector (ASPC) method:
>
> ASPC order: 1
>
> B(1) = 2.500000
> B(2) = -2.000000
> B(3) = 0.500000
>
> Parameters for the always stable predictor-corrector (ASPC) method:
>
> ASPC order: 1
>
> B(1) = 2.500000
> B(2) = -2.000000
> B(3) = 0.500000
>
> Extrapolation method: ASPC
>
> SCF WAVEFUNCTION OPTIMIZATION
>
> ----------------------------------- OT
> ---------------------------------------
> Allowing for rotations
> Minimizer : CG : conjugate gradient
> Preconditioner : FULL_KINETIC : inversion of T + eS
> Precond_solver : DEFAULT
> Line search : 2PNT : 2 energies, one gradient
> stepsize : 0.15000000 energy_gap :
> 0.00100000
> eps_taylor : 0.10000E-15 max_taylor :
> 4
> ----------------------------------- OT
> ---------------------------------------
>
> Step Update method Time Convergence Total energy
> Change
>
> ------------------------------------------------------------------------------
>
> HFX_MEM_INFO| Est. max. program size before HFX [MiB]:
> 18930
> HFX_MEM_INFO| Number of cart. primitive ERI's calculated:
> 38624794188272
> HFX_MEM_INFO| Number of sph. ERI's calculated:
> 5756863922070
> HFX_MEM_INFO| Number of sph. ERI's stored in-core:
> 5727923021897
> HFX_MEM_INFO| Number of sph. ERI's stored on disk:
> 0
> HFX_MEM_INFO| Number of sph. ERI's calculated on the fly:
> 0
> HFX_MEM_INFO| Total memory consumption ERI's RAM [MiB]:
> 5164770
> HFX_MEM_INFO| Whereof max-vals [MiB]:
> 1233
> HFX_MEM_INFO| Total compression factor ERI's RAM:
> 8.46
> HFX_MEM_INFO| Total memory consumption ERI's disk [MiB]:
> 0
> HFX_MEM_INFO| Total compression factor ERI's disk:
> 0.00
> HFX_MEM_INFO| Size of density/Fock matrix [MiB]:
> 128
> HFX_MEM_INFO| Size of buffers [MiB]:
> 2
> HFX_MEM_INFO| Number of periodic image cells considered:
> 33
> HFX_MEM_INFO| Est. max. program size after HFX [MiB]:
> 18871
>
> 1 OT CG 0.15E+00 337.0 0.00012275 -7323.9604751264
> -7.32E+03
> 2 OT LS 0.77E-01 20.9 -7323.9605963412
> 3 OT CG 0.77E-01 21.3 0.00005254 -7323.9619119441
> -1.44E-03
> 4 OT LS 0.69E-01 21.1 -7323.9621490010
> 5 OT CG 0.69E-01 21.3 0.00003333 -7323.9621521424
> -2.40E-04
> 6 OT LS 0.65E-01 21.0 -7323.9622430025
> 7 OT CG 0.65E-01 21.3 0.00001976 -7323.9622432955
> -9.12E-05
> 8 OT LS 0.58E-01 21.0 -7323.9622712907
> 9 OT CG 0.58E-01 21.2 0.00001132 -7323.9622717428
> -2.84E-05
> 10 OT LS 0.68E-01 21.1 -7323.9622824556
> 11 OT CG 0.68E-01 21.2 0.00000720 -7323.9622826949
> -1.10E-05
> 12 OT LS 0.73E-01 21.1 -7323.9622874241
> 13 OT CG 0.73E-01 21.2 0.00000482 -7323.9622874446
> -4.75E-06
> 14 OT LS 0.82E-01 21.0 -7323.9622898107
> 15 OT CG 0.82E-01 21.2 0.00000382 -7323.9622898422
> -2.40E-06
> 16 OT LS 0.73E-01 21.0 -7323.9622911751
> 17 OT CG 0.73E-01 21.3 0.00000296 -7323.9622911933
> -1.35E-06
> 18 OT LS 0.81E-01 21.0 -7323.9622920761
> 19 OT CG 0.81E-01 21.2 0.00000231 -7323.9622920831
> -8.90E-07
> 20 OT LS 0.93E-01 21.2 -7323.9622926954
>
> Leaving inner SCF loop after reaching 20 steps.
>
> Electronic density on regular grids: -1727.9999999402
> 0.0000000598
> Core density on regular grids: 1727.9999999265
> -0.0000000735
> Total charge density on r-space grids: -0.0000000137
> Total charge density g-space grids: -0.0000000137
>
> Overlap energy of the core charge distribution:
> 0.00000000000265
> Self energy of the core charge distribution:
> -14074.58786311355834
> Core Hamiltonian energy:
> 4408.80717501710569
> Hartree energy:
> 4095.52826292682403
> Exchange-correlation energy:
> -671.83062536674151
> Hartree-Fock Exchange energy:
> -1081.87924215901262
>
> Total energy:
> -7323.96229269538162
>
> outer SCF iter = 1 RMS gradient = 0.23E-05 energy =
> -7323.9622926954
>
> ----------------------------------- OT
> ---------------------------------------
> Allowing for rotations
> Minimizer : CG : conjugate gradient
> Preconditioner : FULL_KINETIC : inversion of T + eS
> Precond_solver : DEFAULT
> Line search : 2PNT : 2 energies, one gradient
> stepsize : 0.15000000 energy_gap :
> 0.00100000
> eps_taylor : 0.10000E-15 max_taylor :
> 4
> ----------------------------------- OT
> ---------------------------------------
>
> Step Update method Time Convergence Total energy
> Change
>
> ------------------------------------------------------------------------------
> 1 OT CG 0.15E+00 43.0 0.00000211 -7323.9622927063
> -6.23E-07
> 2 OT LS 0.47E-01 20.9 -7323.9622916813
> 3 OT CG 0.47E-01 21.2 0.00000134 -7323.9622929669
> -2.61E-07
> 4 OT LS 0.10E+00 21.0 -7323.9622931292
> 5 OT CG 0.10E+00 21.2 0.00000129 -7323.9622931964
> -2.29E-07
> 6 OT LS 0.85E-01 21.0 -7323.9622933660
> 7 OT CG 0.85E-01 21.4 0.00000115 -7323.9622933731
> -1.77E-07
> 8 OT LS 0.87E-01 21.0 -7323.9622935183
> 9 OT CG 0.87E-01 21.2 0.00000099 -7323.9622935185
> -1.45E-07
>
> *** SCF run converged in 9 steps ***
>
> Electronic density on regular grids: -1727.9999999401
> 0.0000000599
> Core density on regular grids: 1727.9999999265
> -0.0000000735
> Total charge density on r-space grids: -0.0000000136
> Total charge density g-space grids: -0.0000000136
>
> Overlap energy of the core charge distribution:
> 0.00000000000265
> Self energy of the core charge distribution:
> -14074.58786311355834
> Core Hamiltonian energy:
> 4408.80711518344106
> Hartree energy:
> 4095.52826732740959
> Exchange-correlation energy:
> -671.83060828648809
> Hartree-Fock Exchange energy:
> -1081.87920462925604
>
> Total energy:
> -7323.96229351845068
>
> outer SCF iter = 2 RMS gradient = 0.99E-06 energy =
> -7323.9622935185
> outer SCF loop converged in 2 iterations or 29 steps
>
> Integrated absolute spin density :
> 2.0000037692
> Ideal and single determinant S**2 : 2.000000
> 2.000000
>
> HFX_MEM_INFO| Number of cart. primitive DERIV's calculated:
> 171964164039744
> HFX_MEM_INFO| Number of sph. DERIV's calculated:
> 39581123230020
> HFX_MEM_INFO| Number of sph. DERIV's stored in-core:
> 0
> HFX_MEM_INFO| Number of sph. DERIV's calculated on the fly:
> 39581123230020
> HFX_MEM_INFO| Total memory consumption DERIV's RAM [MiB]:
> 0
> HFX_MEM_INFO| Whereof max-vals [MiB]:
> 16
> HFX_MEM_INFO| Total compression factor DERIV's RAM:
> 0.00
>
> ENERGY| Total FORCE_EVAL ( QS ) energy (a.u.):
> -7323.962293636419417
>
> -------- Informations at step = 3 ------------
> Optimization Method = BFGS
> Total Energy = -7323.9622936364
> Real energy change = -0.0007083471
> Predicted change in energy = -0.0002188809
> Scaling factor = 0.0000000000
> Step size = 0.0453787275
> Trust radius = 0.4724315332
> Decrease in energy = YES
> Used time = 2379.563
>
> Convergence check :
> Max. step size = 0.0453787275
> Conv. limit for step size = 0.0030000000
> Convergence in step size = NO
> RMS step size = 0.0037943120
> Conv. limit for RMS step = 0.0015000000
> Convergence in RMS step = NO
> Max. gradient = 0.0042154388
> Conv. limit for gradients = 0.0004500000
> Conv. for gradients = NO
> RMS gradient = 0.0002954283
> Conv. limit for RMS grad. = 0.0003000000
> Conv. in RMS gradients = YES
> ---------------------------------------------------
>
> As you see the 'Used time' of each ionic step is much larger than the sum
> of the OT steps.
>
>
> Here is my input:
>
> &GLOBAL
> PROJECT_NAME NaCl
> RUN_TYPE GEO_OPT
> PRINT_LEVEL MEDIUM
> &END GLOBAL
> &FORCE_EVAL
> METHOD QS
> &DFT
> BASIS_SET_FILE_NAME GTH_BASIS_SETS
> POTENTIAL_FILE_NAME GTH_POTENTIALS
> WFN_RESTART_FILE_NAME NaCl-RESTART.wfn
> ROKS
> MULTIP 3
> &QS
> EPS_PGF_ORB 1.0e-12
> &END
> &MGRID
> CUTOFF 1400
> REL_CUTOFF 40
> &END MGRID
> &XC
> &XC_FUNCTIONAL PBE0
> &END XC_FUNCTIONAL
> &HF
> &MEMORY
> MAX_MEMORY 32000
> &END
> &SCREENING
> EPS_SCHWARZ 1.0e-8
> SCREEN_ON_INITIAL_P TRUE
> &END
> &INTERACTION_POTENTIAL
> POTENTIAL_TYPE TRUNCATED
> CUTOFF_RADIUS 6.0
> T_C_G_DATA t_c_g.dat
> &END
> &END
> &END XC
> &SCF
> MAX_SCF 20
> EPS_SCF 1.0e-6
> CHOLESKY INVERSE
> SCF_GUESS RESTART
> &OT
> ROTATION
> PRECONDITIONER FULL_KINETIC
> ENERGY_GAP 0.001
> &END OT
> &OUTER_SCF
> EPS_SCF 1.0e-6
> MAX_SCF 30
> &END OUTER_SCF
> &END SCF
> &END DFT
> &SUBSYS
> &CELL
> ABC [angstrom] 16.92 16.92 16.92
> ALPHA_BETA_GAMMA [deg] 90 90 90
> PERIODIC XYZ
> SYMMETRY CUBIC
> &END CELL
> &TOPOLOGY
> COORD_FILE_FORMAT XYZ
> COORD_FILE_NAME 11.xyz
> &END TOPOLOGY
> &KIND Na
> ELEMENT Na
> BASIS_SET DZVP-GTH
> POTENTIAL GTH-PBE-q9
> &END KIND
> &KIND Cl
> ELEMENT Cl
> BASIS_SET DZVP-GTH
> POTENTIAL GTH-PBE-q7
> &END KIND
> &END SUBSYS
> &END FORCE_EVAL
>
>
>
>
> Best,
> Xiaoming
>
>
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