Embed Size (px)
Citation preview
分子動力学シミュレーションa0*(�F9;L�.�QZ]_bQ^`��0*e�4/�e6 !�0*e� ���QZ]_bQ^`
a� ���cMDdQZ]_bQ^`,�G� a� F�=AV]bT`G5��)�O/:e?MKGHLI8O�JL<CBe"2G� \PVR[O/�>Lf
$� 3 PbY`UWS]bX &7���
a�%+�-e'#/�e�.��10ED��FN@Lf
Arai et al., J. Chem. Phys. (2007)Winarto et al., Nanoscale 7, 12659 (2015) Hirano et al., BioPhys J. (2010)Yamamoto et al., Phys. Rev. E (2014).
分子動力学シミュレーションの高速化v��� �jqrtwjsu^NRdBI@68_�>)�vG%H�^�M;�]@6ikm
5Hv%H_2X_$�Ocjqrtwjsu_�.�f<M�=PKd{
v�>)8x"2��"�7�y^NRdjqrtwjsu_JE�5Hf��UYD�Z@6f<Mxkwnwiuorwl_1y
v�>)8^NRd+-0 +-_0 `tghpumZKdPz�>)8Zjqrtwjsuf<MS[Zz�Q_+-f?,{0 F4^XLYz/C[jqrtwjsu9'_#��f3AVdS[^ �{Ayuba et al., J. Chem. Phys., 149, 044504 (2018)
vG%Hjqrtwjsu_JE�%H^�UYz5H_bM^��v��VdS[`�/���:{�%H�a�*]\z@6�_��P!(TeYLdPz&W�Q_@6%Hf=Vd{
���!+ ���!+
�
����#%(+�&)
����#%(+�&)
��������
� ��"
機械学習を用いた分子動力学シミュレーションの高速化
Thirty-Second AAAI Conference on Artificial Intelligence, 2192 (2018).https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16477
*MD-GAN�����������Generative adversarial nets (GANs),��������$!' MD-GAN���.����#%(+�&)!+ ����-����#%(+�&)!+ ����$!'.
, Arjovsky et al., arXiv preprint, 1701.07875 (2017).
MD-GANの概要
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6
…
t = 1 t = 3t = 2
…
Feature extraction Step skip
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6
…
MD data
MD-GAN …t = 1 t = 5
T��&MUJ*D��1?,/7MDHOPRUHQS*DX 9�!4.GB5�39�&���G��6,F=("�+�Y��;��:��1E;6<9-X2;�#V#��W+8;C):>E@)*:��Y
#��- Feature extraction: N�;�;A6��;��$+�@E9D=X2FDG#��71EY- Step skip: MILKN'=0;���;A6��;��$+�@E9D=X2FDG#��71EY
#��;�&���G��0X%�&;���G��1EY
Libration Bend Stretch
6Tanzi L. et al., J. Phys. Chem. 116, 10160(2012).
適用例: 水の振動スペクトル
�9� �MD)3(�"�!#'+%*/�9� �MD)3(�"�!#'+%*/
Frequency [1/512 step]
Inte
nsity
[a.u
.]
� ����MD&,-03&.1$� ���7��'+%*/6 ��$���84���91107�9305 K7�2�����5
適用例: 水の振動スペクトル! "
!
!"#!$""#$ %&$ ' ("!&")*
!%
(
"
Figure 4: OH vibrational spectra of water molecules in theequilibrium bulk system. (A) Snapshot of the system con-taining 110 water molecules. (B) Schematic view of vibra-tional motion of the water molecule. (C) OH relative veloc-ities of the MD (top) and generated data by our model (bot-tom). Blue, green, and red lines represent x, y, and z compo-nents of the velocity vector, respectively. (D) OH vibrationalspectra of water molecules using the MD and generated timeseries. The spectra were obtained by the Fourier transformof the OH relative velocity correlation function. Insets showthat larger training data reduce the noise of spectrum.
has a generator without latent variables and a discriminator.In this experiment, the dimensions of the latent variable wasset to be 16. Let us investigate the behavior of the latent vari-able. Figure 3C shows transitions of the latent variable in thegeneration of z after training. The x and y axes show thirdand fourth dimension of the latent variable, and the yellowand red denote whether the second dimension of the latentvariable was greater or less than 0.5 at t = 3, respectively.At t = 0, all the latent variable were generated from theuniform distribution. After the initialization, the distributionof z reached a stationary distribution through our generatorGz . We can identify a periodic structure in the stationarydistribution of z, and this is one of the example where thelatent variable successfully extract the interesting structuresin the target system. This advantage of our model will con-tribute to an understandings of the system behavior.
Water vibrational spectraNext, we applied our model to a more complex system:the bulk water. Water molecules are an important target ofresearch in chemical, physical, and biological fields. Be-cause of thermodynamic fluctuations and interactions with
other molecules, the OH bonds of water molecules have spe-cific vibrational motions. We performed ab initio MD sim-ulations, which is an MD method on the basis of ab ini-tio energy calculations, for the bulk water (see Fig. 4A).To test the applicability for real time series, we used theOH motions as an input and calculated vibrational spec-tra using the generated time series. For the ab initio MDsimulations, we used the CPMD code (Hutter and Ian-nuzzi 2005) using the Car-Parrinello method (Car and Par-rinello 1985). In the CPMD simulations, the Predew-Burrke-Ernzerhof functional was used to approximate the exchange-correlation terms (Perdew, Burke, and Ernzerhof 1996), andwe described the valence-core interaction using the Martins-Troullier pseudo-potentials (Troullier and Martins 1991).The CPMD simulation was conducted under the isothermaland iso-volume conditions (305 K), and the volume of thesystem was predefined by the classical isothermal and iso-baric classical MD simulation using the NAMD 2.9 soft-ware (Phillips et al. 2005) with the TIP3P water model (Jor-gensen et al. 1983). In this experiment, the OH relative ve-locities were prepared as input for our model, and our modelgenerated time series of OH velocities. A notable point isthat input velocities are not long time enough to calculatethe statistic (M = 64 steps = 61.92 fs). Figure 4C showsthe OH velocities of the MD and generated data in the wa-ter molecules. As this figures shows, the vibrational motionof the water molecules is complex. Vibrational spectra wereobtained by taking the Fourier transform of the OH rela-tive velocity correlation function (the vibrational density ofstates) (Tanzi, Ramondo, and Guidoni 2012),
P (ω) =N!
k=1
" ∞
−∞⟨rk(0)rk(t)⟩eiωtdt,
where ri(0)ri(t) is the time series velocity auto-correlationfunction and ⟨⟩ is the ensemble average. Figure 4D showsOH vibrational spectra from the MD and generated timeseries of OH motion in water molecules. The OH vibra-tional motion is characterized by three modes: libration(600 cm−1), bend (1500 cm−1), and stretch (3200 cm−1)motions (see Fig. 4B). In the spectra given by CPMD, weidentified three peaks corresponding to these modes. No-tably, the generated motion also contained this information,and there are three clear peaks with precise frequencies. Fur-thermore, the external forms of the frequency distribution,including slopes and intensities, matched each other. Realvibrational motion includes anharmonic combinations of thepeaks, and interactions with external environments make thespectra significantly complex. Under this environment, ourmodel precisely generated the time series of OH bonds, andwe could obtain physical and important dynamical statisticsusing the generated time series. Unfortunately, there is oneunexpected peak at around 8300 cm−1. This peak is unphys-ical and can be attributed to the bias. Note that larger train-ing data reduce a noise of the libration peak (see Fig. 4Dinsets).
2196
���-��
- Feature extraction: OH��-��� - Step skip: 0.97 fs112547+&01282547:= 124.16 fs;-���1��693+%)<��8��1�('=
Long MD data
Generated data
��,� -.0/!: �����;1��&0$+"*#'=
���"(! ��"(!
MD-GAN
4��������
適用例: 水の振動スペクトル
Inte
nsity
[a.u
.]
Inte
nsity
[a.u
.]
Frequency [1/512 step]Frequency [1/512 step]
�� %�#':OH�������������$(&�� ����
C Takahashi et al., Polymers 9, 24(2017).
適用例: ポリマーの拡散現象7<46=>A1405 g/molB300�+��&21�,#"*MD59:=@5;>3 "D���� �AMSDB-��3 )(EA��F500 KD��?������B
7<8@�+.D�/�",01�+����AMSD-�%B$!�'1CE
(�)��
��)MDAH=
����%�*�
!".$
!%
(�)MD,7���798MSD
MD-GAN468MSD��!�
��AH=
20�5+$:��
��AH=
time [ps]
MSD
[a.u
.]
����5%�:��/8-34�L
適用例: ポリマーの拡散現象'� 5&�M- Feature extraction: CD;>EF��5����- Step skip: 30 ps:1<@?B3/8128<@?BI= 3.84 nsJ5� �:��AH=3.2K "G��:#10L
まとめと今後の展望• 分子動力学シミュレーションを時間方向に高速化するための機械学習モデル MD-GANを開発した．
• MD-GANによる高速化は，長時間相関をもつ物性の計算において特に有用である．
• 様々な分子種に対して短時間の大規模計算を行い，その長時間化をMD-GANで行うことで，分子動力学シミュレーションを用いた新規材料開発等の加速が期待できる．
• MD-GANの適用事例を増やしつつ改良を行うことで，将来的に他の時系列データ予測への応用も検討する．
