Aidan Thompson, Sandia National lab

1. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly
owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
SNAP: Automated Generation of High-accuracy
Interatomic Potentials Using Quantum Data
Aidan Thompson
Center for Computing Research,
Sandia National Laboratories,
Albuquerque, New Mexico
Approved for public release under SAND2018-2573 C, SAND2018-2067 C

2. Collaborators
2
Steve
Plimpton
Stan Moore
Axel Kohlmeyer
....Many Others
Laura Swiler
Stephen Foiles
Garritt Tucker
Adam Stephens
Christian Trott
Mitch Wood
Mary Alice Cusentino
SNAP Potentials

3. Outline of This Talk
3
Introduction
• LAMMPS
• Interatomic Potentials
SNAP Potentials
• Structure
• Accuracy
• Computational Performance
• Future Work
Conclusions

4. What is Molecular Dynamics Simulation?
4
Distance
Time
Å m
10-15syears
QM
MD
MESO
Design
MD Engine
HNS
atoms,
positions,
velocities
interatomic potential
Positions, velocities
and forces at many
later times
• Continuum models require underlying
models of the materials behavior
• Quantum methods can provide very
complete description for 100s of atoms
• Molecular Dynamics acts as the “missing
link”
• Bridges between quantum and continuum
models
• Moreover, extends quantum accuracy to
continuum length scales; retaining atomistic
information
constraints

5. What is Molecular Dynamics Simulation?
Time
Å
10-15s
QM
MD
MESO
Design
Distance

6. What is Molecular Dynamics Simulation?
6
Distance
Time
Å m
10-15syears
QM
MD
MESO
Design
MD Engine
HNS
atoms,
positions,
velocities
interatomic potential
Positions, velocities
and forces at many
later times
• Continuum models require underlying
models of the materials behavior
• Quantum methods can provide very
complete description for 100s of atoms
• Molecular Dynamics acts as the “missing
link”
• Bridges between quantum and continuum
models
• Moreover, extends quantum accuracy to
continuum length scales; retaining atomistic
information
constraints

7. What is Molecular Dynamics Simulation?
7
Distance
Time
Å m
10-15syears
QM
MD
MESO
Design
• Continuum models require underlying
models of the materials behavior
• Quantum methods can provide very
complete description for 100s of atoms
• Molecular Dynamics acts as the “missing
link”
• Bridges between quantum and continuum
models
• Moreover, extends quantum accuracy to
continuum length scales; retaining atomistic
information
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Thanks to Aidan Thompson
F=ma
Large-scale Atomic/Molecular
Massively Parallel Simulator
•" Biomolecules
•" Polymers (soft
materials)
•" Materials science
(hard materials)
•" Mesoscale to
continuum
Mike
Chandross

8. Historical Development for Potentials
Moore’s Law for Interatomic Potentials
Plimpton and Thompson, MRS Bulletin (2012).
Moore’s Law for potentials
CHARMm
EAM
Stillinger-Weber
Tersoff
AIREBO
MEAM
ReaxFF eFF
COMB
EIM
BOP
GAP
REBO
SPC/E
1980 1990 2000 2010
Year Published
10
-6
10
-5
10
-4
10
-3
10
-2
Cost[core-sec/atom-timestep]
Old
SNAP
New
SNAP
8
Twobody (B.C.)
Lennard-Jones
Hard Sphere
Coulomb
Bonded
Manybody (1980s)
Stillinger-Weber
Tersoff
Embedded Atom Method
Advanced (90s-2000s)
REBO
BOP
COMB
ReaxFF
Big/Deep/Machine
Data/Learning (2010s)
GAP, SNAP, NN,…
Drivers
• Increased computer resources
• Application to Real Materials
• Quantum Methods

9. Historical Development for Potentials
9
Twobody (B.C.)
Lennard-Jones
Hard Sphere
Coulomb
Bonded
Manybody (1980s)
Stillinger-Weber
Tersoff
Embedded Atom Method
Advanced (90s-2000s)
REBO
BOP
COMB
ReaxFF
Big/Deep/Machine
Data/Learning (2010s)
GAP, SNAP, NN,…
Computational Cost
Error
LJ
EAM
MEAM
SNAP GAP
J.Chem.Phys. 148, 241401 (2018): Special Topic on
Data-Enabled Theoretical Chemistry
Guest edited by Rupp, von Lilienfeld, and Burke

10. Outline of This Talk
10
Introduction
• LAMMPS
• Interatomic Potentials
SNAP Potentials
• Structure
• Accuracy
• Performance
• Future Work
Conclusions

11. • GAP (Gaussian Approximation Potential): Bartok, Csanyi et al., Phys. Rev. Lett, 2010. Uses
3D neighbor density bispectrum and Gaussian process regression.
• SNAP (Spectral Neighbor Analysis Potential): Our SNAP approach uses GAP’s neighbor
bispectrum, but replaces Gaussian process with linear regression.
- More robust
- Lower computational cost
- Decouples MD speed from training set size
- Enables large training data sets, more bispectrum coefficients
- Straightforward sensitivity analysis
- Equivalent to Gaussian process or kernel ridge regression with dot-product kernel
ESNAP
= Ei
SNAP
i=1
N
∑ + φij
rep
rij( )
j<i
N
∑
Ei
SNAP
= β0 + βkBi
k
k∈ J<Jmax{ }
∑
Geometric
descriptors
of atomic
environments
Energy as a
function of
geometric
descriptors
SNAP: Spectral Neighbor Analysis Potentials
9
Bispectrum
components:
2-, 3-, 4-body
site features

12. SNAP Fitting Process
FitSnap.py
12
Dakota
optimization,
sensitivity
“Hyper-parameters”
• Cutoff distance
• Group Weights
• Number of Terms
• Etc.
fitsnap.py
Communicate with
LAMMPS; weighted
regression to obtain
SNAP coefficients
LAMMPS
Low/High
Throughput
DFT
Metrics
• Force residuals
• Energy residuals
• Elastic constants
• Etc.
Bispectrum
components &
derivatives,
reference potential

13. SNAP Tantalum
• Training data:
• Energy, force, stress
• ~5,000 data points
• Deformed crystals phases
• Generalized stacking faults
• Surfaces
• Liquid
• Excellent agreement with training
data, e.g. Liquid RDF
• Peierls barrier is the activation energy
to move a screw dislocation
• Not included in training data
• SNAP potential agrees well with DFT
calculations
A. P. Thompson , L.P. Swiler, C.R. Trott,
S.M. Foiles, and G.J. Tucker, J. Comp.
Phys., 285 316 (2015) .
13

14. 14
Training SNAP for Alloys
– Tungsten+Beryllium
Elastic Deformations
• ~5400 configurations
DFT-MD Trajectories
• ~3500 configurations
Amorphous
Liquids
Surfaces
• Plasma-surface interactions in ITER
• Tungsten planned divertor material
• Beryllium planned first wall material
• Plasma causes redeposition of Be into W
• The focus of the joint potential
has been on ordered phases of
WBe
• B2(WBe), L12(WBe3), C14(WBe2),
C15(WBe2), C36(WBe2) and
D2b(WBe2)
L12C14
C15
C36

15. 15
Tungsten Properties
Be Elastic Moduli Be Phase Stability Be Defect Formation
Training SNAP for Transferability – WBe
Candidate 18584:
Predicts the correct WBe intermetallic phases
(stable Laves phases, unstable B2 and L12)
Key drawbacks are Be-elastic and W-vacancy
properties.

16. 16
Be Implantation into W surfaces
Preliminary Results17
- MD simulations of 75 eV Be implantation in W at 1000 K in a 10 x 10 x 40
◦ Place Be randomly in x and y direction and run for 3 ps
◦ Output whether Be reflected or implanted and compare with SRIM
MD simulations of 75 eV Be implantation in W
1000 K in a 10 x 10 x 40 box
◦ Random position above surface, initial velocity normal to surface
◦ Run MD for 3 ps, collect statistics over 1000s of trials
◦ Capture rate, implantation depth
◦ Compare with SRIM

17. 0 10 20 30
k
0
1
2
3
4
5
<||∆j
Σβk
B
i
k
||>
B(j1
,j2
,j)
B(j1
,j1
,j)
B(j,0,j)
17
Effect of High-Order Bispectrum Components
• MD simulation of molten tantalum using SNAP Ta06A potential
• Magnitude of average force contributed by each bispectrum
component

18. 18
Effect of High-Order Bispectrum Components
0 5 10 15
Band Limit 2Jmax
0
100
200
300
400
500
600
Cij
[GPa]
C11
C12
C44
0 5 10 15
Band Limit 2Jmax
0
100
200
300
400
500
600
Cij
[GPa]
• Elastic constants for tantalum versus band limit
Linear SNAP Quadratic SNAP

19. 19
Adding Descriptors Increases Cost A Lot
10 100 1000
# SNAP Descriptors (K)
0.01
0.1
1
10
100
1000
Performance[10
3
atom-steps/s]
Intel Haswell
Intel KNL
AMD CPU
IBM PowerPC
y~x
-2
10 100 1000
# SNAP Descriptors (K)
0.01
0.1
1
10
100
1000
Performance[10
3
atom-steps/s]
NVIDIA K20X
NVIDIA P100
y~x
-2
y~x
-2
y~x
-2
y~x
-1
CPU GPU
• Benchmarks for Exascale Computing Project
• Short MD simulation of BCC tungsten @ 300K
• GPU and KNL use the LAMMPS Kokkos package
• 2000 atoms, 1 node

20. What About Adding Quadratic Terms?
• Linear terms are 4-body
• Quadratic terms are 7-body
• Number of linear coefficients grows as O(J3)
• Number of quadratic coefficients grows as = O(J6)
• Energy, force, stress remain linear in b and a
• Can still use linear least squares (SVD)
• Number of columns will increase from K to K(K+1)/2
Wood and Thompson,
J. Chem.Phys., 148 241721 (2018)
https://arxiv.org/abs/1711.11131
SNAP Tantalum
2 meV/atom
5 meV/A

21. What About Adding Quadratic Terms?
• Cross-validation analysis to control for overfitting
• Training and Testing errors for the GSF(110) subset of the DFT data
• All potentials fit to a large, diverse, set of DFT data for tantalum
• 2J=8
GSF(112) Energy GSF(112) Force

22. Can We Improve Multi-Element SNAP?
Etot = Eref +
NX
i=1
Ei
SNAP
Ei
SNAP = ↵ · Bi
, i is element ↵
=
X
{ }
KX
k=1
k,↵ B ,i
k
Fj
SNAP =
X
{ }
KX
k=1
k,↵
NX
i=1
@B ,i
k
@rj
ujmm0 = Ujmm0 (0, 0, 0) +
X
rii0 < Rcut
i0 2
fc(rii0 )w Ujmm0 (✓0, ✓, )
Bj1j2j =
j1X
m1,m0
1= j1
j2X
m2,m0
2= j2
j
X
m,m0= j
(ujmm0 )⇤
H
jmm0
j1m1m0
1
j2m2m0
2
uj1m1m0
1
uj2m2m0
2
1. No need to use w factors
2. For two elements, for each Bk, the 4 variants are BAAA
k , BAAB
k , BABB
k ,
BBBB
Etot = Eref +
NX
i=1
Ei
SNAP
Ei
SNAP = ↵ · Bi
, i is element ↵
=
X
{ }
KX
k=1
k,↵ B ,i
k
Fj
SNAP =
X
{ }
KX
k=1
k,↵
NX
i=1
@B ,i
k
@rj
ujmm0 = Ujmm0 (0, 0, 0) +
X
rii0 < Rcut
i0 2
fc(rii0 )w Ujmm0 (✓0, ✓, )
Bj1j2j =
j1X
m1,m0
1= j1
j2X
m2,m0
2= j2
j
X
m,m0= j
(ujmm0 )⇤
H
jmm0
j1m1m0
1
j2m2m0
2
uj1m1m0
1
uj2m2m0
2
1. No need to use w factors
2. For two elements, for each Bk, the 4 variants are BAAA
k , BAAB
k , BABB
k ,
BBBB
uj
m,m0 = Uj
m,m0 (0, 0, 0) +
X
rii0 <Rcut
fc(rii0 )wiUj
m,m0 (✓0, ✓, ) (4)
The expansion coe cients uj
m,m0 are complex-valued and they are not
directly useful as descriptors, because they are not invariant under rotation
of the polar coordinate frame. However, the following scalar triple products
of expansion coe cients can be shown to be real-valued and invariant under
rotation [7].
Bj1,j2,j =
j1X
m1,m0
1= j1
j2X
m2,m0
2= j2
j
X
m,m0= j
(uj
m,m0 )⇤
H
jmm0
j1m1m0
1
j2m2m0
2
uj1
m1,m0
1
uj2
m2,m0
2
(5)
The constants H
jmm0
j1m1m0
1
j2m2m0
2
are coupling coe cients, analogous to the Clebsch-
Gordan coe cients for rotations on the 2-sphere. These invariants are the
components of the bispectrum. They characterize the strength of density
correlations at three points on the 3-sphere. The lowest-order components
5
Current Multi-element SNAP
All elements lumped together in
density expansion
Proposed Multi-Element SNAP
Elemental
Weight
Elemental
Expansion
Coefficient
Three-Element
Bispectrum
Component
Ei
SNAP = ↵ · Bi
, i is element ↵
=
KX
k=1
k,↵Bi
k
Fj
SNAP =
KX
k=1
k,↵
NX
i=1
@Bi
k
@rj
ujmm0 = Ujmm0 (0, 0, 0) +
X
ri0 < Rcut
fc(ri0 )w Ujmm0 (✓0, ✓, )
Bj1j2j =
j1X
m1,m0
1= j1
j2X
m2,m0
2= j2
j
X
m,m0= j
(ujmm0 )⇤
H
jmm0
j1m1m0
1
j2m2m0
2
uj1m1m0
1
uj2m2m0
2
1. No need to use w factors
2. For two elements, for each Bk, the 4 variants are BAAA
k , BAAB
k , BABB
k ,
BBBB
k
3. For N elements, the number of variants is the number of ways of select-
ing 3 from N with repetition, also called the number of arrangements of
3 stars and N 1 bars, which is N+3 1
3
i.e. 1, 4, 10, 20 = Tetrahedral
number N(N + 1)(N + 2)/6
4. Enumeration pattern is increment rightmost position less than N and
repeat that value in all positions to the right: 111, 112, 113, 122, 123,
133, 222, 223, 333

23. 23
Fully-Automated Generation of SNAP
• Manage QM data
generation
• SimHyperParams (E, V,
N, R0)
• Bootstrapping
• Latin Hypercube
Sampling
• Some user input
required
Trajectory Farm
FitSNAP.py
• SNAP FitHyper
Params (rcut)
• Genetic Algorithm
• Training Errors
• Cross-validation
• Generates new QM data, returns SNAP potentials

24. Conclusions
§ Application needs are driving demand for more accurate potentials
§ SNAP ML potentials balance efficiency and accuracy
§ Lowest order bispectrum components (2Jmax<=6) are most important
§ Adding higher-order bispectrum descriptors does not help/hurt much
§ Quadratic terms improve accuracy in training and out-of-sample testing
§ Ongoing work: more automation and multi-element SNAP
§ Biggest challenge: "good" data, and lots of it
Acknowledgements:
Mitch Wood (SNAP Development)
Mary Alice Cusentino (SNAP Testing)
Steve Plimpton (LAMMPS)
24

25. Extra Slides
25

26. SNAP GPU Performance
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Number of Atoms
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
Speed(Atom-Timesteps/sec)
LAMMPS running on a CPU machine
1 node (36 x 2.1 GHz Intel Broadwell)
1.2 TFlops peak
50% efficiency
200 atoms/node
50% efficiency
50 atoms/GPU
ExaMiniMD running on a GPU machine
1 GPU (NVIDIA P100)
5.3 TFlops peak

27. 27
Pareto Optimal Potentials
• For material properties of interest within a set
of SNAP potentials
• Increase in accuracy w/ number of bispectrum
components used
• How about when comparing potentials?
• Resources are limited, which is your best choice?
Computational Cost
Errorw.r.t.DFT
LJ
EAM
MEAM
SNAP GAP

28. SNAP Data-Driven Interatomic Potentials for Materials
PI: Aidan Thompson, Mitch Wood (post-doc), many others
SNAP Fitting Process• Quantum (QM) materials calculations can handle 100s of atoms
• Classical molecular dynamics (MD) can handle millions of atoms
• Limited by accuracy of interatomic potentials (IAP)
• Simple potentials (LJ, EAM) good for qualitative behavior
• Machine-learning potentials can approximate QM
• SNAP balances accuracy and cost
• Current Applications:
• Fusion energy materials (EXAALT ECP project, with LANL)
• Phase change kinetics
• Shock mechanics
Distance
Time
Å m
10-15syears
QM
MD
MESO
Design
Computational Cost
Error
L
J
EAM
MEAM
SNAP GA
P
Qualitative
Properties
Near QM
Accuracy
MD simulation of helium bubble
formation near tungsten
surface

29. Two philosophical extremes in the
development of interatomic potential models
• Functional forms based on
fundamental understanding of
electronic origins of bonding
• Bond Order Potentials (BOP)
• Model Generalized Pseudopotential
Theory (MGPT)
• COMB
• ReaxFF
• …
• Gives confidence that it will
interpolate/extrapolate reasonably
• Empirical fit of a flexible functional
form
• Gaussian Approximation Potentials
(GAP)
• Spectral Neighbor Analysis Potential
(SNAP) - this work
• …
• Replaces the need for intuition/art
with extensive computation
• Automate the fitting process?
• Apply across multiple materials classes?
Luke: Is the dark side stronger?
Yoda: No, no no. Quicker, easier,
more seductive.
The Force!
Darth Vader: You underestimate the
power of the dark side!
The Dark Side!
Borrowed from
Stephen Foiles
and Lucasfilm 29