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Advancing first-principle symmetry-guided nuclear modeling for studies of nucleosynthesis and fundamental symmetries in nature

NCSA Blue Waters Symposium for Petascale Science and Beyond, 2018

Students & Postdocs Collaborators

Nuclear Physics Nuclear Physics

neutron proton

Accurate tests of fundamentals laws of nature

Nuclear interactions Discovery potential in nuclear physics

Residual strong force → highly complex two-, three- and four-body forces Properties and reactions of nuclei at the edge of their existence Universal internucleon interaction derived from QCD

Applications of Applications of Nuclear Structure & Reaction Modeling Nuclear Structure & Reaction Modeling

Nuclear reactions for applied energy studies

Neutrino studies Dark matter experiments

Fusion energy

Standard Model & physics beyond

X-ray bursts Astrophysics: thermonuclear processes in the cosmos Neutrino & Cosmology research

Ab initio Ab initio Approaches to Nuclear Structure and Reactions Approaches to Nuclear Structure and Reactions

Many-body dynamics Nuclear reactions Realistic nuclear potential models Strong interaction

Energy

3H 3H 4He 2H

n

¼

wave functions nuclear properties reaction rates cross sections

Ab Initio Ab Initio No-Core Shell Model No-Core Shell Model

Solve the non-relativistic quantum problem of A-interacting nucleons

Goal:

Calculate nuclear properties from resulting eigenvectors Use resulting eigenvectors for ab initio nuclear reaction studies

• 2. Compute Hamiltonian matrix
• 3. Find lowest-lying eigenvalues and eigenvectors [Lanczos algorithm]

1+ 2+ 0+ 4+

• 1. Choose physically relevant model space and construct its basis

jÃi =

N

X

i = 1

ci jÁi i

Additional steps

Key Challenge Key Challenge

Limits application of ab initio studies to lightest nuclei Use partial symmetries of nuclear collective motion to adopt smaller physically relevant model spaces

Computational Scale Explosion Why symmetry-adapted approach? Why Blue Waters?

Large aggregate memory and amount of memory per node (64GB) High peak memory bandwidth (102.4 GB/s)

[courtesy of Pieter Maris]

Many-nucleon basis natural for description of many-body dynamics of nuclei

N Sp Sn S L

number of harmonic oscillator excitations total proton, total neutron and total intrinsic spins deformation rotation

Many-nucleon basis natural for description of many-body dynamics of nuclei

Symmetry-Adapted No-Core Shell Model Symmetry-Adapted No-Core Shell Model

MPI/OpenMP Implementation of Symmetry-Adapted No-Core Shell Model MPI/OpenMP Implementation of Symmetry-Adapted No-Core Shell Model

Excellent scalability

1 process 15 processes 378 processes 37,950 processes

Load balanced computations

Computational effort: 80 % - computing matrix elements 10% - solving eigenvalue problem

Implementation

C++/Fortran code parallelized using hybrid MPI/OpenMP Open source: https://sourceforge.net/p/lsu3shell/home/Home/

(0 0) (1 1) (0 3) (3 0) (2 2) (1 4) (4 1) (3 3) (0 6) (6 0) (2 5) (5 2) (4 4) (7 1) (6 3) (9 0) (8 2) (10 1) (12 0) 0.0% 0.3% 0.5% (0 1) (2 0) 0% 60% (1 0) (0 2) (2 1) (4 0) 0% 7% 14% (0 0) (1 1) (0 3) (3 0) (2 2) (4 1) (6 0) 0% 5% 10% (0 1) (2 0) (1 2) (3 1) (0 4) (2 3) (5 0) (4 2) (6 1) (8 0) 0% 2% 4% (1 0) (0 2) (2 1) (1 3) (4 0) (3 2) (0 5) (2 4) (5 1) (4 3) (7 0) (6 2) (8 1) (10 0) 0.00% 0.75% 1.50%

( 1 ) ( 2 ) ( 1 2 ) ( 3 1 ) ( 4 ) ( 2 3 ) ( 5 ) ( 4 2 ) ( 1 5 ) ( 3 4 ) ( 6 1 ) ( 7 ) ( 5 3 ) ( 2 6 ) ( 4 5 ) ( 8 ) ( 7 2 ) ( 6 4 ) ( 9 1 ) ( 8 3 ) ( 1 1 ) ( 1 2 ) ( 1 2 1 ) ( 1 4 )

0.00% 0.06% 0.11%

remaining Sp Sn S Sp=1/2 Sn=3/2 S=2 Sp=3/2 Sn=1/2 S=2 Sp=3/2 Sn=3/2 S=3 Sp=1/2 Sn=1/2 S=1

60.77% 18.82% 11.63% 5.37% 2.28% 0.85% 0.27%

6Li : 1+ gs

Discovery: Emergence of Simple Patterns in Complex Nuclei Discovery: Emergence of Simple Patterns in Complex Nuclei

Dytrych, Launey, Draayer, et al., PRL 111 (2013) 252501

Low spin Large deformation

Key features of nuclear structure Model space truncation

SA-NCSM on BlueWaters: reaching towards medium mass nuclei SA-NCSM on BlueWaters: reaching towards medium mass nuclei

Nuclear density Excitation Spectrum Binding energy

Complete space: Symmetry-adapted space:

SA-NCSM on BlueWaters: reaching towards medium mass nuclei SA-NCSM on BlueWaters: reaching towards medium mass nuclei

Complete space dimension: dimension:

complete selected

Novae and X-ray bursts

Astrophysical Nucleosynthesis Astrophysical Nucleosynthesis

Astrophysical Nucleosynthesis Astrophysical Nucleosynthesis

Calculation of reaction rates Calculation of reaction rates

SA-NCSM

Probability to find cluster structure

Nuclear reaction:

Calculation of reaction rates Calculation of reaction rates

Blue Waters

Probability to find cluster structure astrophysical simulation

Nuclear reaction:

Response function Response function

Nucleus response to external probe (photon, neutrino, etc ..)

SA-NCSM SA-NCSM

New approach: SA-NCSM + Lorentz Integral Transform Method

Response functions for neutrino studies Response functions for neutrino studies

Response functions – input for neutrino experiments Nuclear input - 2nd largest source of uncertainties SA-NCSM + LIT: preliminary results : component of neutrino detectors

Code improvements Code improvements

Dynamic memory allocation optimizations

Dynamic allocation – generally slow, and dependend on malloc implementation.

malloc replacement

We tested tcmalloc (Google), jemalloc (Facebook), tbbmalloc (Intel)

SA-NCSM – lot of concurrent small allocations

tcmalloc – best performance & memory footprint decrease

Memory pooling Small buffer optimizations

allocations of a lot of small objects is inneficient request a big block of memory and do bookkeeping ourselves Boost.Pool provides convenient classes for managing memory pools use a small static buffer for a small number of elements, and only requests dynamic memory when we go over the specified threshold.

Code improvements Code improvements

Nearly factor of 2 speedup 10-15% decrease of total memory footprint

20Ne J=0 20Ne J=2 16O J=0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 legacy code

• ptimized code

speedup

Summary Summary

Key challenges

Description of 99.9% mass of the Universe

Why it matters

Ultimate source of energy in the Universe Aggregate memory and high memory bandwidth

Why Blue Waters

Many papers in top journals and reaching beyond what competitives theories could accomplish

Accomplishments Blue Waters team contributions

Excellent support and guidance as needed

Broader impacts

Training next generation of STEM workforce

Shared Data

Codes and results publicly available

Products

https://sourceforge.net/p/lsu3shell/home/Home/