Performance and compute resources

Table of Contents

Cc4s is designed to run highly parallel coupled cluster calculations. It allows calculations with far more than 100 electrons on modern high performance computing clusters. Currently, Cc4s can not benefit from GPUs or other accelerators. Note: although OpenMP threading is generally supported it is recommended to set

export OMP_NUM_THREADS=1

In the following we present a way to estimate the required compute resources for models with arbitrary system sizes that can be chosen to reflect the dimensions of any targeted ab initio system. In this manner Cc4s does not require actual input files for the specific ab initio system. The computational complexity can be estimated on two levels. First, a dry calculation can be performed which gives a first overview of the time and memory consumptions of the calculation. Thereafter, a full calculation can be performed to examine the performance on the target system. Note that the performance depends heavily on the hardware, network, compilers, and libraries.

1. Generating the input file

The only input required are the dimensions of the desired calculation. It is important to note that the performance depends only on the dimensions of the system as given below. Physical properties (periodic vs. molecular system, low bandgap vs. high bandgap, etc.) have no impact.

The most important system parameter is the number of electrons used in the post Hartree–Fock calculation (core electrons are typically not considered). In vasp the number of valence electrons of a given atom is given in the POTCAR file (ZVAL); the other electrons are treated within the frozen-core approximation (https://www.vasp.at/wiki/index.php/POTCAR). In a closed-shell calculation the number of occupied orbitals \(N_o\) is half the number of valence electrons \(N_\text{elec}\). When using the basis-set correction typically 8-16 virtual orbitals per occupied orbital are needed to obtain converged results (see Ref. (Irmler, Gallo, and Grüneis 2021)). Further input parameter is the number of field variables of the vertex \(N_\text{F}\). It has been shown that for converged results this number can be chosen as small as 2-3 times \(N_v\).

An exemplary snippet of the algorithm creating the required vertex reads

- name: UegVertexGenerator
  in:
    No: 123
    Nv: 1114
    NF: 2000
    halfGrid: 1
    rs: 2
  out:
    eigenEnergies: EigenEnergies
    coulombVertex: CoulombVertex

The value for \(r_s\) can be chosen to be any positiv real number (it will be irrelevant for the performance analysis). The pseudo-boolean variable halfGrid is chosen to be \(1\) for $Γ$-point or molecular calculations, and \(0\) for arbitrary $k$-point calculations where the wavefunctions is complex.

A full input file for a CCSD calculation can be found at (https://gitlab.cc4s.org/cc4s/cc4s/-/raw/master/test/tests/ueg/rs1.0-123occ-1114virt/cc4s.in).

2. Dry and full calculation

The generated input file can either be used in a dry calculation (running a few seconds on a laptop device), or in a real calculation on the desired target machine.

The dry calculation is called with the following command:

$Cc4s -i cc4s.in -d 1536

In this example we obtain an output for 1536 mpi ranks. The output stream reads

                __ __
     __________/ // / _____
    / ___/ ___/ // /_/ ___/
   / /__/ /__/__  __(__  )
   \___/\___/  /_/ /____/
  Coupled Cluster for Solids

version: heads/develop-0-g3467f0ad-dirty, date: Mon Mar 28 11:40:04 2022 +0200
build date: Mar 29 2022 16:27:07
compiler: g++ (Ubuntu 10.3.0-1ubuntu1~20.10) 10.3.0
total processes: 1
calculation started on: Mon Apr  4 11:16:08 2022

Dry run finished. Estimates provided for 1536 ranks.
Memory estimate (per Rank/Total): 1.51836 / 2332.2 GB
Operations estimate (per Rank/Total): 912374 / 1.40141e+09 GFLOPS
Time estimate with assumed performance of 10 GFLOPS/core/s: 91237.4 s (25.3437 h)
--

The number of mpi ranks can be adjusted based on the memory/walltime constrains. Note that the given memory and time estimates can differ in the real calculation and should only be used as an educated guess. The obtained performance depends heavily on the hardware (CPU, network, …). The actual memory requirements can be higher than estimated. Using only 50-75% of the total available memory has shown to be a reasonable choice.

The full calculation is called by the following command:

mpirun -np $ranks $Cc4s -i cc4s.in

3. Exploited benchmarks

We have examined the performance of Cc4s on two different clusters both using different Intel Xeon CPUs. For the weak scaling benchmark the number of occupied orbitals was increased with growing node count. The number of virtuals per occupied was set to 12 in all calculations. The number of field variables per virtual was kept almost constant at a value of around 3.5.

Table 1: Weak scaling of CCSD on Irene with Intel Skylake 8168 CPUs.
#Nodes #Cores \(N_o\) Memory (GB/core) Performance (GFLOPS/core/s)
1 48 40 2.0 18.7
4 192 64 2.4 20.1
16 768 80 1.4 21.4
20 960 96 2.0 21.4
50 1296 108 1.4 20.2
100 4800 128 1.4 19.4
Table 2: Weak scaling of CCSD on raven with Intel CascadeLake 9242 CPUs.
#Nodes #Cores \(N_o\) Memory (GB/core) Performance (GFLOPS/core/s)
1 72 40 1.3 19.8
4 288 64 1.6 22.3
8 576 80 1.9 25.1
16 1152 96 1.7 20.2
32 2304 108 1.5 27.1
48 3456 128 1.9 26.1
64 4608 140 1.8 22.0
80 5760 152 2.0 29.8
Table 3: Strong scaling on of CCSD raven \(N_o=123\), \(N_v=1114\), \(N_F=2000\)
#Nodes #Cores Memory (GB/core) Performance (GFLOPS/core/s)
12 864 1.40 31.1
16 1152 1.05 29.7
24 1728 0.70 23.9
30 2160 0.56 21.1
40 2880 0.42 20.8
48 3456 0.35 18.6
64 4608 0.26 16.0
72 5184 0.23 17.2
80 5760 0.21 14.8

4. Literature

Irmler, Andreas, Alejandro Gallo, and Andreas Grüneis. 2021. “Focal-Point Approach with Pair-Specific Cusp Correction for Coupled-Cluster Theory.” The Journal of Chemical Physics 154 (June): 234103. doi:10.1063/5.0050054.

Created: 2022-09-19 Mon 15:00