Deep Learning for Multiscale Molecular Modeling Linfeng Zhang - PowerPoint PPT Presentation

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 Introduction 1 Deep Potential 2 Deep Potential Generator (DP-GEN) 3 Free energy and Reinforced Dynamics 4 Conclusions 5 Linfeng Zhang (PU) DL for MMM June 2019 2 / 42

Outline Introduction 1 Deep Potential 2 Deep Potential Generator (DP-GEN) 3 Free energy and Reinforced Dynamics 4 Conclusions 5 Linfeng Zhang (PU) DL for MMM June 2019 3 / 42

Where deep learning could help? d 0 , 0 d 1 , 0 d 2 , 0 x 0 d 0 , 1 d 1 , 1 F ( x ) d 2 , 1 x 1 d 0 , 2 d 1 , 2 d 2 , 2 d 0 , 3 d 1 , 3 L 0 L 1 L 2 L out x F ( x ) d 0 d 1 d 2 W p · d p − 1 + b p � d p = L p ( d p − 1 ) = φ � Composition of analytical and nonlinear functions; Approximator for High-D functions. Linfeng Zhang (PU) DL for MMM June 2019 4 / 42

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. Linfeng Zhang (PU) DL for MMM June 2019 5 / 42

Accuracy v.s. efficiency dilemma PES as an example: E = E ( r 1 , ..., r i , ..., r N ) . First principle: accurate but very expensive. For example KS-DFT, ∼ 10 2 atoms: E = � Ψ 0 | H KS | Ψ 0 � , e Empirical potentials: fast but limited accuracy. For example Lennard-Jones potential E = 1 V ij = 4 ǫ [( σ ) 12 − ( σ � ) 6 ] . V ij , 2 r ij r ij i � = j Lennard-Jones, J. E. (1924), Proc. R. Soc. Lond. A, 106 (738): 463477 Linfeng Zhang (PU) DL for MMM June 2019 6 / 42

Two important aspects Deep learning could help for a classical of problems in multi-scale molecular modeling. 1 � min l ( f w , f ) �D� w i ∈D deep learning model f w ; dataset D ; definition of l and optimization algorithm. Linfeng Zhang (PU) DL for MMM June 2019 7 / 42

Outline Introduction 1 Deep Potential 2 Deep Potential Generator (DP-GEN) 3 Free energy and Reinforced Dynamics 4 Conclusions 5 Linfeng Zhang (PU) DL for MMM June 2019 8 / 42

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. Linfeng Zhang (PU) DL for MMM June 2019 9 / 42

Typical construction � E = E i , E i = E s ( i ) ( r i , { r j } j ∈N ( i ) ) , N ( i ) = { j : r ij = | r ij | ≤ r c } i E i ( r i , { r j } j ∈N ( i ) ) represented by fully connected NNs with symmetrized inputs. Behler, J., Parrinello, M. (2007). Phys. Rev. Lett., 98(14), 146401. Linfeng Zhang (PU) DL for MMM June 2019 10 / 42

Descriptors: Local coordinates atom j R e z ij z atom i e y ij e x y ij x ij or Han, et.al., CiCP, 23, 629 (2018). Zhang, et.al., PRL, 120, 143001 (2018) Linfeng Zhang (PU) DL for MMM June 2019 11 / 42

Descriptors: a smooth descriptor by DNN Key: complete and adaptive. Translation and Rotation: ( R i ( R i ) T ) : Ω i jk = r ji · r ki , Permutation: ( ( G i 1 ) T R i ) : � j ∈N ( i ) g ( r ji ) r ji , Finally, we propose: D i = ( G i 1 ) T R i ( R i ) T G i 2 . Zhang, et.al., NeurIPS 2018 Linfeng Zhang (PU) DL for MMM June 2019 12 / 42

Various systems with the same principle Zhang, et.al., NeurIPS 2018 Linfeng Zhang (PU) DL for MMM June 2019 13 / 42

Different thermodynamic conditions The path integral water structures (ambient cond.) 3.5 0.8 DeePMD O−O DeePMD DeePMD O−H 0.7 DFT 3.0 DeePMD H−H 0.6 DFT O−O 2.5 DFT O−H 0.5 RDF g(r) DFT H−H 2.0 P( ψ ) 0.4 1.5 0.3 1.0 0.2 0.5 0.1 0.0 0.0 0 1 2 3 4 5 6 0.5 1 1.5 2 2.5 3 r [Å] ψ [rad] Ice in different thermodynamic states 6.0 6.0 6.0 DeePMD O−O DeePMD O−O DeePMD O−O DeePMD O−H DeePMD O−H DeePMD O−H 5.0 5.0 5.0 DeePMD H−H DeePMD H−H DeePMD H−H DFT O−O DFT O−O DFT O−O 4.0 DFT O−H 4.0 DFT O−H 4.0 DFT O−H RDF g(r) DFT H−H RDF g(r) DFT H−H RDF g(r) DFT H−H 3.0 3.0 3.0 2.0 2.0 2.0 1.0 1.0 1.0 0.0 0.0 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 r [Å] r [Å] r [Å] 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) Linfeng Zhang (PU) DL for MMM June 2019 14 / 42

Extension to coarse-graining 3.0 AIMD DeePMD 2.0 DeePCG k DeePCG (large sys.) g(r) 1.0 0.0 AIMD (r) 0.05 0.00 g(r) - g -0.05 -0.10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z r [nm] r c = 0.27 nm r c = 0.37 nm 1.6 0.8 x 1.4 AIMD 0.7 DeePMD 1.2 0.6 DeePCG 1.0 0.5 j P( θ ) 0.8 0.4 i(a) 0.6 0.3 i 0.4 0.2 0.2 0.1 0.0 0.0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 r c = 0.456 nm r c = 0.60 nm y 0.7 0.6 0.6 0.5 i(b) 0.5 0.4 P( θ ) 0.4 0.3 0.3 0.2 0.2 0.1 0.1 Zhang et.al. J. Chem. Phys., 149, 034101 (2018) 0.0 0.0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 θ / π θ / π Linfeng Zhang (PU) DL for MMM June 2019 15 / 42

Extension to electronic information Linfeng Zhang (PU) DL for MMM June 2019 16 / 42

Extension to electronic information Linfeng Zhang (PU) DL for MMM June 2019 17 / 42

Extension to nonadiabatic excited state dynamics Chen, Wen-Kai, et al. J. P. C. Lett. 9.23 (2018): 6702-6708. Linfeng Zhang (PU) DL for MMM June 2019 18 / 42

Combined with metadynamics L. Bonati and M. Parrinello, Phys. Rev. Lett. 121, 265701 Linfeng Zhang (PU) DL for MMM June 2019 19 / 42

Extension to T-dependent free energy Linfeng Zhang (PU) DL for MMM June 2019 20 / 42 (in preparation)

Extension to T-dependent free energy Left: Radial distribution functions (RDFs); Right: Rankine-Hugoniot curve. (a) (b) 3 , 11 eV 4.5 g/cm 3 , 2 eV 6.0 g/cm 1 1 g (r) 10 4 AIMD N=32 DPMD N=32 FPMD DPMD N=256 DPMD 0 0 10 3 Cauble 0 1 2 3 4 0 1 2 3 4 Pressure (Mbar) Nellis RaganIII (c) (d) 3 , 1000 eV 8.1 g/cm 3 , 200 eV 7.5 g/cm 10 2 1 1 g(r) 1 10 0 0 0 10 0 1 2 3 0 1 2 3 4 3 4 5 6 7 8 r (Å) r (Å) 3 ) Density (g/cm (in preparation) Linfeng Zhang (PU) DL for MMM June 2019 21 / 42

Deep Potential: MD scalability 10 5 g 10 4 DFT n CPU core time per step [s] i l a c S 10 3 c i b u 10 2 C Linear Scaling 10 1 DeePMD 10 0 10 -1 DeePMD DFT: PBE0+TS 10 -2 10 1 10 2 10 3 10 4 10 5 10 6 Number of molecules Linfeng Zhang (PU) DL for MMM June 2019 22 / 42

Open source software DeePMD-kit TensorFlow: efficient network operators LAMMPS, i-PI; MPI/GPU support. Free download from https://github.com/deepmodeling/deepmd-kit Comp.Phys.Comm., 0010-4655 (2018). Linfeng Zhang (PU) DL for MMM June 2019 23 / 42

Outline Introduction 1 Deep Potential 2 Deep Potential Generator (DP-GEN) 3 Free energy and Reinforced Dynamics 4 Conclusions 5 Linfeng Zhang (PU) DL for MMM June 2019 24 / 42

Two important aspects, revisited 1 � min l ( f w , f ) �D� w i ∈D deep learning model f w ; dataset D ; definition of l and optimization algorithm. Linfeng Zhang (PU) DL for MMM June 2019 25 / 42

Active learning: the DP-GEN scheme Training/Fitting : model/representation. Exploration : sampler and error indicator; DPMD and model deviation � �� f i − � f i �� 2 � ǫ = max i Labeling : ab initio calculator. Example: Al-Mg alloy 0.0044 % explored confs. are labeled Zhang et.al. Phys. Rev. Mat. 3, 023804 Linfeng Zhang (PU) DL for MMM June 2019 26 / 42

DP-GEN: test of Al 3.5 1.2 3.0 1.0 2.5 0.8 Surface formation energy by DP/MEAM [J/m 2 ] 1.2 2.0 0.6 1.1 4 5 6 7 1.5 1 1.0 0.9 Exp. 943K 0.5 DP 943K MEAM 943K 0.8 0.0 2 3 4 5 6 7 8 9 10 11 12 13 14 0.7 r [Å] DP: FCC Al 0.6 DP: HCP Mg 12 MEAM: FCC Al EXP 0.5 10 DP MEAM: HCP Mg MEAM ν (THz) 8 0.4 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 6 Surface formation energy by DFT [J/m 2 ] 4 2 0 Γ X K Γ L q Linfeng Zhang (PU) DL for MMM June 2019 27 / 42

DP-GEN: tests based on Materials Project Linfeng Zhang (PU) DL for MMM June 2019 28 / 42

DP-GEN: tests based on Materials Project Linfeng Zhang (PU) DL for MMM June 2019 29 / 42

Irradiation damage simulation Linfeng Zhang (PU) DL for MMM June 2019 30 / 42