Advancing first-principle symmetry-guided nuclear modeling for - PowerPoint PPT Presentation

Advancing first-principle symmetry-guided nuclear modeling for studies of nucleosynthesis and fundamental symmetries in nature Students & Postdocs Collaborators NCSA Blue Waters Symposium for Petascale Science and Beyond, 2018

Nuclear Physics Nuclear Physics proton neutron Nuclear interactions Residual strong force → highly complex two-, three- and four-body forces Discovery potential in nuclear physics Universal internucleon interaction derived from QCD Properties and reactions of nuclei at the edge of their existence Accurate tests of fundamentals laws of nature

Applications of Nuclear Structure & Reaction Modeling Nuclear Structure & Reaction Modeling Applications of Astrophysics: thermonuclear processes in the cosmos X-ray bursts Nuclear reactions for applied energy studies Fusion energy Neutrino & Cosmology research Standard Model & physics beyond Neutrino studies Dark matter experiments

Ab initio Approaches to Nuclear Structure and Reactions Approaches to Nuclear Structure and Reactions Ab initio Strong interaction Nuclear reactions Many-body dynamics n 2 H Energy 0 ¼ 3 H 3 H 4 He wave functions Realistic reaction rates nuclear properties nuclear potential cross sections models

Ab Initio No-Core Shell Model No-Core Shell Model Ab Initio Goal: Solve the non-relativistic quantum problem of A-interacting nucleons 1. Choose physically relevant model space and construct its basis 2. Compute Hamiltonian matrix 3. Find lowest-lying eigenvalues and eigenvectors [Lanczos algorithm] 4 + X N 2 + j Ãi = c i jÁ i i 1 + i = 1 0 + Additional steps Calculate nuclear properties from resulting eigenvectors Use resulting eigenvectors for ab initio nuclear reaction studies

Key Challenge Key Challenge Computational Scale Explosion [courtesy of Pieter Maris] Limits application of ab initio studies to lightest nuclei Why Blue Waters? Large aggregate memory and amount of memory per node (64GB) High peak memory bandwidth (102.4 GB/s) Why symmetry-adapted approach? Use partial symmetries of nuclear collective motion to adopt smaller physically relevant model spaces

Symmetry-Adapted No-Core Shell Model Symmetry-Adapted No-Core Shell Model Many-nucleon basis natural for description of many-body dynamics of nuclei Many-nucleon basis natural for description of many-body dynamics of nuclei N number of harmonic oscillator excitations S p S n S total proton, total neutron and total intrinsic spins deformation L rotation

MPI/OpenMP Implementation of Symmetry-Adapted No-Core Shell Model MPI/OpenMP Implementation of Symmetry-Adapted No-Core Shell Model Implementation C++/Fortran code parallelized using hybrid MPI/OpenMP Open source: https://sourceforge.net/p/lsu3shell/home/Home/ Computational effort: 80 % - computing matrix elements 10% - solving eigenvalue problem Load balanced computations 1 process 15 processes 378 processes 37,950 processes Excellent scalability

Discovery: Emergence of Simple Patterns in Complex Nuclei Discovery: Emergence of Simple Patterns in Complex Nuclei 0.11% 6 L i : 1 + 0.06% gs 0.27% 0.00% ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 0 2 1 3 0 2 5 4 1 3 6 0 5 2 4 8 7 6 9 8 1 1 1 1 1 0 2 4 1 0 2 1 4 3 0 2 5 4 1 7 3 6 5 0 2 4 1 3 0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 2 1 0 ) ) ) ) 0.5% 0.3% 0.85% 0.0% (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) 1.50% 0.75% 2.28% 0.00% (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) Key features of nuclear structure 4% Low spin 2% 5.37% Large deformation 0% (0 1) (2 0) (1 2) (3 1) (0 4) (2 3) (5 0) (4 2) (6 1) (8 0) 10% 5% Model space truncation 11.63% 0% (0 0) (1 1) (0 3) (3 0) (2 2) (4 1) (6 0) remaining Sp Sn S 14% Sp=1/2 Sn=3/2 S=2 7% 18.82% Sp=3/2 Sn=1/2 S=2 Sp=3/2 Sn=3/2 S=3 0% (1 0) (0 2) (2 1) (4 0) Sp=1/2 Sn=1/2 S=1 60% 60.77% 0% (0 1) (2 0) Dytrych, Launey, Draayer, et al., PRL 111 (2013) 252501

SA-NCSM on BlueWaters: reaching towards medium mass nuclei SA-NCSM on BlueWaters: reaching towards medium mass nuclei Excitation Spectrum Nuclear density 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 Novae and X-ray bursts complete selected dimension: Complete space dimension:

Astrophysical Nucleosynthesis Astrophysical Nucleosynthesis

Astrophysical Nucleosynthesis Astrophysical Nucleosynthesis

Calculation of reaction rates Calculation of reaction rates Nuclear reaction: SA-NCSM Probability to find cluster structure

Calculation of reaction rates Calculation of reaction rates Nuclear reaction: Blue Waters Probability to find cluster structure astrophysical simulation

Response function Response function Nucleus response to external probe (photon, neutrino, etc ..) New approach: SA-NCSM + Lorentz Integral Transform Method SA-NCSM SA-NCSM

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

Code improvements Code improvements Dynamic memory allocation optimizations Dynamic allocation – generally slow, and dependend on malloc implementation. SA-NCSM – lot of concurrent small allocations malloc replacement We tested tcmalloc (Google), jemalloc (Facebook), tbbmalloc (Intel) tcmalloc – best performance & memory footprint decrease Memory pooling 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 Small buffer optimizations 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 2 1.8 1.6 1.4 1.2 speedup legacy code 1 optimized code 0.8 0.6 0.4 0.2 0 20Ne J=0 20Ne J=2 16O J=0 10-15% decrease of total memory footprint

Summary Summary Key challenges Description of 99.9% mass of the Universe Why it matters Ultimate source of energy in the Universe Why Blue Waters Aggregate memory and high memory bandwidth Accomplishments Many papers in top journals and reaching beyond what competitives theories could accomplish 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/