Towards Atomistic Modeling of Complex Environments with Many-Body Machine Learning Potentials

Alex M. Maldonado

September 1, 2022

aalexmmaldonado

Keith Group

Clean energy is growing, but slowly

Advancing energy technologies

Nuclear power

Molten salts

Nuclear Reactor by Olena Panasovska from Noun Project

Batteries

Electrolyte by M. Oki Orlando from Noun Project

Charge carriers and electrolytes

Park, C.; et al. J. Power Sources 2018, 373, 70-78. DOI: 10.1016/j.jpowsour.2017.10.081

Lv, X.; et al. Chem. Phys. Lett. 2018, 706, 237-242. DOI: 10.1016/j.cplett.2018.06.005

Fuel production

Solvation plays an important role

Catalysts

Ma, C.; et al. ACS Catal. 2012, 373, 1500-1506. DOI: 10.1021/cs300350b

Accelerating exploration with solvents

Computational modeling

Cost

AIMD

Classical MD

Implicit/explicit

Implicit

Confidence

Cost

Screening

approach

Promising candidates

Search space

without experimental data

Solvation treatments

Confidence requires explicit (MD) methods

Goal

Explicit solvation

Lv, X.; et al. Chem. Phys. Lett. 2018, 706, 237-242. DOI: 10.1016/j.cplett.2018.06.005

Let's model a molten salt

DFT

N^{3-4}

MP2

N^5

CCSD(T)

N^7

Pro: Fast

Con: Parameters

Classical potential

Quantum chemistry

Pro: Accurate

Con: Cost

We need a new method

Confidence

2x atoms

128x cost

Machine learning potentials

Structure

ML potential

Energy and forces

Quantum

chemistry

Machine learning potentials

Calculate total energies with QC

Training a typical ML potential

Sample tens of thousands of configurations

Approximation: atomic contributions can reproduce total energy

Examples: DeePMD, GAP, SchNet, PhysNet, ANI, . . .

E_{total} \approx \sum\limits^{N_{atoms}} \varepsilon_i

Known

Learned

with a local descriptor

Machine learning potentials

Training with a global descriptor

Local

Global

Encodes each

atom

Encodes entire

structure

increased data efficiency

Many descriptors and parameters

Single descriptor

Machine learning potentials

Training on forces provides more information about the geometry and energy relationship

Chimiela, S. ; et al. Sci. Adv. 2017, 3 (5), e1603015. DOI: 10.1126/sciadv.1603015

Gradient-domain machine learning (GDML)

Better interpolation

Global descriptor

Training on forces

requires 1 000 structures instead of 10 000+

Machine learning potentials

System size is still a limiting factor

Global

Fewer structures enables higher levels of theory

CCSD(T)

Local

Tons of sampling

CCSD(T)

What we want

What we can afford

Descriptor

Size transferable?

CCSD(T)

How can we make GDML potentials size transferable?

Transferability with n-body interactions

-76.31270

-76.31251

-76.31273

-228.96298

-0.00831

-0.00705

-0.00700

-228.93794

(-0.02504)

-228.96031

(-0.00267)

1 body

1+2 body

3-body

Add energy

Remove energy

All energies are in Hartrees

Many-body expansion (MBE)

MBE: the total energy of a system is equal to the sum of all n-body interactions

Truncate

E =

\sum E_i^{(1)}

\sum\Delta E_{ij}^{(2)}

\sum \Delta E_{ijk}^{(3)}

+ \cdots

Unlocks size transferability for highly accurate methods

CCSD(T)

Many-body expansion (MBE)

Training a many-body GDML (mbGDML) potential

Sample a thousand

configurations

Calculate n-body energy (+ forces) with QC

Calculate total energies with QC

Known

E_{total} \approx \sum E_i^{(1)} + \sum\Delta E_{ij}^{(2)} + \sum \Delta E_{ijk}^{(3)}

E_{total} \approx \sum\limits^{N_{atoms}} \varepsilon_i

Known

Learned

Reproduce physical n-body energies

Approximation: atomic contributions can reproduce total energy

Incorporates more physics into our ML potentials

Sample tens of thousands of configurations

Our innovation

Less training data
Use higher levels of theory
Easy to parallelize

Many-body expansion framework accelerated with GDML

Unique opportunity with GDML accuracy and efficiency

If successful

keithgroup.github.io/mbGDML/

Case study

Modeling three common solvents

Water (H2O)

Acetonitrile (MeCN)

Methanol (MeOH)

Training set

1 000 structures

(instead of 10 000+)

Sampling

n-body structures from GFN2-xTB simulations

Level of theory

MP2/def2-TZVP

ORCA v4.2.0

Case study - Results

Isomer rankings

Which tetramer (4mer) has the lowest energy (i.e., global minimum)?

Requires accurate relative energies

Isomer #1

Isomer #2

Isomer #3

Case study - Results

Tetramer rankings

(per monomer)

System	Energy RMSE [kcal/mol]	Force RMSE [kcal/(mol A)]
(H2O)4	0.82 (0.20)	0.78 (0.07)
(MeCN)4	0.29 (0.07)	0.16 (0.01)
(MeOH)4	1.37 (0.34)	1.49 (0.06)

(per atom)

Many-body GDML accurately captures relative energies

Info: We desire methods with less than 2 kcal/mol error

Does mbGDML scale to larger systems?

System	Energy Error [kcal/mol]	Force RMSE [kcal/(mol A)]
(H2O)16	4.01 (0.25)	1.12 (0.02)
(MeCN)16	0.28 (0.02)	0.35 (0.004)
(MeOH)16	5.56 (0.35)	1.79 (0.02)

Case study - Results

Consistent normalized errors

Size transferable

Case study - Results

Radial distribution function (rdf)

What we want

g(r)

Tells us if we are getting the correct liquid structure

Case study - Results

Many-body GDML accurately captures liquid structure

137 H2O molecules

67 MeCN molecules

61 MeOH molecules

Reminder: We have only trained on clusters with up to three molecules

Time for 10 ps MeCN simulation:

mbGDML 19 hours

\approx

MP2 23 762 years

\approx

20 ps NVT MD simulations; 1 fs time step; Berendsen thermostat at 298 K

Conclusions

Explicit solvent modeling without experimental data

Classical

Ab initio

mbGDML

Training

Speed

Accuracy

Scaling

Poor

Excellent

Acknowledgments

InSiDe ChEMS group

Dr. John Keith

Dr. Yasemin Basdogan

Dr. Charles Griego

Dr. Emily Eikey

Lingyan Zhao

Barbaro Zulueta

Chinmay Mhatre

Dominick Filonowich

Funding

Office of the Provost