News from this week at Supercomputing
A64FX
The most energy-efficient HPL machine today is pure CPU. It is also among the least “made for HPL” architectures on the list.
https://www.top500.org/green500/list/2019/11/
DAOS filesystem performance
DAOS declares #1 in IO-500 on the basis of performance-per-node (Weka on AWS was absolute performance). They maxed out I/O read bandwidth of the NVDIMMs in their cluster; iops were client limited. Pretty crazy efficiency. #SC19 pic.twitter.com/u1cauolk1y
— Glenn K. Lockwood (@glennklockwood) November 20, 2019
https://www.vi4io.org/io500/start
Force models
$$ V_{LJ}® = 4 \epsilon \Big[ \big(\frac{\sigma}{r}\big)^{12} - \big(\frac{\sigma}{r}\big)^6 \Big] $$
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('ggplot')
# https://pubs.acs.org/doi/abs/10.1021/acs.inorgchem.7b00207
def phi_lj(r):
eps = .4308
sigma = 3.310
return 4*eps*((sigma/r)**12 - (sigma/r)**6)
def phi_buckingham(r):
A = 318418
rho = .294276
C = 2007.88
return A * np.exp(-r/rho) - C/r**6
r = np.linspace(0.01, 10)
plt.plot(r, phi_lj(r), label='LJ');
plt.plot(r, phi_buckingham(r), label='Buckingham')
plt.ylim(-1,1)
plt.legend();
The orbitals of real atoms are far more complicated than a radial function, and depend on other nearby atoms.
Amber is a sophisticated force model evaluator
Amber force fields can be used in other molecular dynamics packages, such as GROMACS and NAMD.
The parameters in the force fields are estimated using optimization, like this (see supplement for coefficient values). Some recent work seeks to use black-box machine learning methods (such as neural networks) to build multi-atom force models similar to the more explicit methods above.
Anton-2
A special-purpose computer for molecular dynamics; winner of the 2014 Gordon Bell Prize at Supercomputing.
Ab initio molecular dynamics
The prior methods were all about molecular dynamics that calculate forces based on positions of nuclei. Ab initio methods solve for electronic structure (electrons are fields/waves for this purpose), which is far more expensive. There are a hierarchy of models. Some examples, in order of increasing expense:
- Density Functional Theory
- Coupled Cluster and Tensor Networks
- Quantum Monte-Carlo
Combined, these methods account for a large fraction of global supercomputing time.