deep learning for multiscale molecular modeling

Deep Learning for Multiscale Molecular Modeling

Linfeng Zhang

Princeton University

June 19 2019, MoD-PMI2019, NIFS

Joint work with Han Wang, Roberto Car, Weinan E

Linfeng Zhang (PU) DL for MMM June 2019 1 / 42

Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

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Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

Linfeng Zhang (PU) DL for MMM June 2019 3 / 42

Where deep learning could help?

d0,0 d1,0

d2,0

x0 d0,1 d1,1

d2,1 F(x)

x1 d0,2 d1,2

d2,2

d0,3 d1,3

x d0 d1 d2 F(x)L0 L1 L2 Lout

dp = Lp(dp−1) = φ(W p · dp−1 + bp

)Composition of analytical and nonlinear functions; Approximator for High-D functions.

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Multi-scale Molecular Modeling

A few examples:

ab initio molecular dynamics (MD):quantum mechanics (QM) to MD, potential energy surface (PES);

Coarse-grained (CG) MD:atoms to CG “particles”, free energy surface (FES)/CG potential;

enhanced sampling/phase transition:atoms to fewer collective variables (CVs), FES.

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Accuracy v.s. efficiency dilemma

PES as an example:

E = E(r1, ..., ri, ..., rN ).

First principle: accurate but very expensive.

For example KS-DFT, ∼ 102 atoms:

E = 〈Ψ0|HKSe |Ψ0〉,

Empirical potentials: fast but limited accuracy.For example Lennard-Jones potential

E =1

2

∑i 6=j

Vij , Vij = 4ε[(σ

rij)12 − (

σ

rij)6].

Lennard-Jones, J. E. (1924), Proc. R. Soc. Lond. A, 106 (738): 463477

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Two important aspects

Deep learning could help for a classical of problems in multi-scalemolecular modeling.

minw

1

‖D‖∑i∈D

l(fw, f)

deep learning model fw;

dataset D;

definition of l and optimization algorithm.

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Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

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Requirement for a reliable PES model

accuracy (e.g. uniform);

efficiency (e.g. linear scaling);

physical constraint (e.g. extensivity, symmetry);

no human intervention/ end-to-end.

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Typical construction

E =∑i

Ei, Ei = Es(i)(ri, rjj∈N (i)), N (i) = j : rij = |rij | ≤ rc

Ei(ri, rjj∈N (i)) represented by fully connected NNs with symmetrizedinputs.Behler, J., Parrinello, M. (2007). Phys. Rev. Lett., 98(14), 146401.

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Descriptors: Local coordinates

ez

ey

ex

z

x

y

ij

ij

ij

ij

atom i

atom j

R

or

Han, et.al., CiCP, 23, 629 (2018). Zhang, et.al., PRL, 120, 143001 (2018)

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Descriptors: a smooth descriptor by DNN

Key: complete and adaptive.

Translation and Rotation: (Ri(Ri)T ): Ωijk = rji · rki,

Permutation: ((Gi1)TRi):∑

j∈N (i) g(rji)rji,

Finally, we propose: Di = (Gi1)TRi(Ri)TGi2.

Zhang, et.al., NeurIPS 2018Linfeng Zhang (PU) DL for MMM June 2019 12 / 42

Various systems with the same principle

Zhang, et.al., NeurIPS 2018

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Different thermodynamic conditionsThe path integral water structures (ambient cond.)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 1 2 3 4 5 6

RD

F g

(r)

r [Å]

DeePMD O−ODeePMD O−HDeePMD H−H

DFT O−ODFT O−HDFT H−H

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.5 1 1.5 2 2.5 3

P(ψ

)

ψ [rad]

DeePMDDFT

Ice in different thermodynamic states

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 1 2 3 4 5 6

RD

F g

(r)

r [Å]

DeePMD O−ODeePMD O−HDeePMD H−H

DFT O−ODFT O−HDFT H−H

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 1 2 3 4 5 6

RD

F g

(r)

r [Å]

DeePMD O−ODeePMD O−HDeePMD H−H

DFT O−ODFT O−HDFT H−H

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 1 2 3 4 5 6

RD

F g

(r)

r [Å]

DeePMD O−ODeePMD O−HDeePMD H−H

DFT O−ODFT O−HDFT H−H

PI-ice, P=1.0 bar, T=273 K; ice P=1.0 bar,T=330 K; ice P=2.13 bar,T=238 K;

Zhang et.al. Phys.Rev.Lett 120 143001 (2018)

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Extension to coarse-graining

z

y

x

k

j

ii(a)

i(b)

Zhang et.al. J. Chem. Phys., 149, 034101 (2018)

0.0

1.0

2.0

3.0

g(r

)

AIMDDeePMDDeePCG

DeePCG (large sys.)

-0.10

-0.05

0.00

0.05

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

g(r

) -

gA

IMD(r

)

r [nm]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1

P(θ

)

rc = 0.27 nm

AIMDDeePMDDeePCG

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

P(θ

)

θ / π

rc = 0.456 nm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

rc = 0.37 nm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

θ / π

rc = 0.60 nm

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Extension to electronic information

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Extension to electronic information

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Extension to nonadiabatic excited state dynamics

Chen, Wen-Kai, et al. J. P. C. Lett. 9.23 (2018): 6702-6708.

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Combined with metadynamics

L. Bonati and M. Parrinello, Phys. Rev. Lett. 121, 265701

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Extension to T-dependent free energy

(in preparation)Linfeng Zhang (PU) DL for MMM June 2019 20 / 42

Extension to T-dependent free energy

Left: Radial distribution functions (RDFs); Right: Rankine-Hugoniotcurve.

0 1 2 3 40

1

( c )

( b )

g (r)

A I M D N = 3 2 D P M D N = 3 2 D P M D N = 2 5 6

( a ) 4 . 5 g / c m 3 , 2 e V

0 1 2 3 40

1

6 . 0 g / c m 3 , 1 1 e V

0 1 2 30

1

8 . 1 g / c m 3 , 2 0 0 e V ( d )

g(r)

r ( Å )0 1 2 3 40

1

7 . 5 g / c m 3 , 1 0 0 0 e V

r ( Å )3 4 5 6 7 81 0 0

1 0 1

1 0 2

1 0 3

1 0 4

Pressu

re (M

bar)

D e n s i t y ( g / c m 3 )

F P M D D P M D C a u b l e N e l l i s R a g a n I I I

(in preparation)

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Deep Potential: MD scalability

10-2

10-1

100

101

102

103

104

105

101

102

103

104

105

106

CP

U c

ore

tim

e p

er

ste

p [s]

Number of molecules

Linear ScalingC

ubic

Sca

ling

DeePMD

DFT: PBE0+TS

DFT

DeePMD

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Open source software DeePMD-kit

TensorFlow: efficient network operators

LAMMPS, i-PI; MPI/GPU support.

Free download from https://github.com/deepmodeling/deepmd-kitComp.Phys.Comm., 0010-4655 (2018).

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Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

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Two important aspects, revisited

minw

1

‖D‖∑i∈D

l(fw, f)

deep learning model fw;

dataset D;

definition of l and optimization algorithm.

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Active learning: the DP-GEN scheme

Training/Fitting:model/representation.

Exploration:sampler and error indicator;DPMD and model deviation

ε = maxi

√〈‖fi − 〈fi〉‖2〉

Labeling:ab initio calculator.

Example: Al-Mg alloy0.0044 % explored confs. arelabeled

Zhang et.al. Phys. Rev. Mat. 3, 023804

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DP-GEN: test of Al

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

2 3 4 5 6 7 8 9 10 11 12 13 14

r [Å]

Exp. 943K

DP 943K

MEAM 943K

4 5 6 7

0.6

0.8

1.0

1.2

0

2

4

6

8

10

12

Γ X K Γ L

ν (

TH

z)

q

EXP

DP

MEAM 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Surf

ace form

ation e

nerg

y b

y D

P/M

EA

M [J/m

2]

Surface formation energy by DFT [J/m2]

DP: FCC Al

DP: HCP Mg

MEAM: FCC Al

MEAM: HCP Mg

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DP-GEN: tests based on Materials Project

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DP-GEN: tests based on Materials Project

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Irradiation damage simulation

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DP-GEN for waterP

ressu

re

Temperature

1 Pa

10 Pa

100 Pa

1 kPa

10 kPa

100 kPa

1 MPa

10 MPa

100 MPa

1 GPa

10 GPa

100 GPa

1 TPa

10 µbar

100 µbar

1 mbar

10 mbar

100 mbar

1 bar

10 bar

100 bar

1 kbar

10 kbar

100 kbar

1 Mbar

10 Mbar0K 50K 100K 150K 200K 250K 300K 350K 400K 450K 500K 550K 600K 650K

-250 °C -200 °C -150 °C -100 °C -50 °C 0 °C 50 °C 100 °C 150 °C 200 °C 250 °C 300 °C 350 °C

Freezing point at 1 atm273.15 K, 101.325 kPa

Boiling point at 1 atm373.15 K, 101.325 kPa

Critical point647 K, 22.064 MPa

Solid/Liquid/Vapour triple point273.16 K, 611.657 Pa

251.165 K, 209.9 MPa256.164 K, 350.1 MPa

272.99 K, 632.4 MPa

355.00 K, 2.216 GPa

238.5 K, 212.9 MPa

248.85 K, 344.3 MPa

218 K, 620 MPa

278 K, 2.1 GPa

100 K, 62 GPa

Solid

Ic Ih

XI(hexagonal)

X

VII

VI

VIII

XVIX

XI(ortho-

rhombic)

II V

III Liquid

Vapour

SI

Ionic. Liq.

2500K

0K 200K 400K 600K

1Pa

1KPa

1MPa

1GPa

T

P

Reference model: DFT at the classical SCAN level;

Starting configurations: relaxed Ice I-XV at T = 0 K and equilibratedliquid at T = 330 K;

Range of thermodynamic conditions: red dashed box;

number of MD snapshots: DPMD exploration: 1.4 billion, DFTcalculation: 32 thousand (∼0.002% of the former).Typical AIMD trajectory: 100 thousand snapshots (50-100 ps).

number of DP-GEN iterations: 100.Linfeng Zhang (PU) DL for MMM June 2019 31 / 42

Thermodynamic integration (TI) for the phasediagram

Special issues: size effect; proton disorder, etc.

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Water phase diagram modeled by DP+SCAN

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High-pressure phases modeled by DP+SCAN

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Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

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Free energy and deep neural networks

Exploring configuration space, phase transition, ...

I high dimensionality of the collective variable space;

I high energy barriers and complex energy landscape.

Metadynamics PNAS 99(20):1256212566, 2002):

Temperature accelerated (Chem. Phys. Lett., 426(1):168175, 2006.)

curse of dimensionality.

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Reinforced dynamics

Potential energy Free energy

Method DP-GEN Reinforced dynamics

Model Deep potential ResNet

Sampler Deep potential MD Biased MD

Label Electronic struct. Restrained MD

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Reinforced dynamics

reinforcement learning: state, action, best policy, reward;

reinforced dynamics (RiD): atomic system, biased potential, FES,model deviation.

ε2(s) =⟨‖F(s)−F(s)‖2

⟩, fi(r) = −∇riU(r)+σ(ε(s(r)))∇riA(s(r)),

Zhang, et.al. J.Chem.Phys 148, 124113 (2018).

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Reinforced dynamics

Left: Tripeptide: brute-force simulation (∼50 µs) v.s. RiD (10 nsbiased + 190 ns restrained):

Right: higher dimensional FES: ala-10 and 20 CVs.

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Outline

1 Introduction

2 Deep Potential

3 Deep Potential Generator (DP-GEN)

4 Free energy and Reinforced Dynamics

5 Conclusions

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Conclusions

Model construction and data exploration for PES and FES;

Useful models: Deep Potential, DP-GEN, reinforced dynamics;check https://github.com/deepmodeling/deepmd-kit

Fundamental problems: quantum many-body problem, DFT,dynamics.

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AcknowledgementsAdvisors

Roberto Car, Weinan E

Collaborators

Han Wang, De-Ye Lin (IAPCM)

Jiequn Han, Yixiao Chen, Hsin-Yu Ko, Marcos Andrade (Princeton),

Wissam A Saidi (Univ. of Pittsburgh), Xifan Wu (Temple)

Mohan Chen, Yuzhi Zhang (Peking Univ.)

Fundings and computational resources

Tiger@Princeton, BIBDR, & NERSC;

ONR grant N00014-13-1-0338, DOE grants DE-SC0008626 andDE-SC0009248, and NSFC grants U1430237 and 91530322;

Computational Chemical Science Center: Chemistry in Solution andat Interfaces (DE-SC0019394).

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