Conclusions - Orbital-Based Deep Learning for Molecular Electronic Structure . 6

Chapter II: Orbital-Based Deep Learning for Molecular Electronic Structure . 6

2.6 Conclusions

Electronic structure methods typically face a punishing trade-off between the prediction accuracy of the method and its computational cost, across all areas of the chemical, biological, and materials sciences. We present a new machine-learning method with the potential to substantially shift that trade-off in favor ofab initio- quality accuracy at low computational cost. OrbNet utilizes a graph neural network architecture to predict high-quality electronic-structure energies on the basis of features obtained from low-cost/minimal-basis mean-field electronic structure methods. The method is demonstrated for the case of predicting𝜔B97X-D/Def2-TZVP energies using GFN1-xTB input features, although it is completely general with respect to both the choice of high-level (including correlated wavefunction) method used for generating reference data and the choice of mean-field method used for feature generation. In comparison to state-of-the-art GNN methods for the prediction of total molecule energies for the QM9 dataset, it is shown that OrbNet provides a 33% improvement in prediction accuracy with the same amount of data relative to the next-most accurate method (DeepMoleNet).[54] And in comparison to the wide array of methods used for predicting relative conformer energies in a realistic and

Table2.3:MAEs(reportedinmeV)forpredictingtheQM9datasetoftotalmolecularenergies.Theemployedlabelsarethepublished values[65]calculatedattheB3LYP/6-31G(2df,p)leveloftheory. TrainingsizeSchNetPhysNetDimeNetDeepMoleNetOrbNetOrbNet(+d) 25k----11.68.08 50k1513--8.225.89 110k148.28.026.15.013.87

Message Passing & Pooling

Decoding Residual

BatchNorm

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Swish

Residual Residual Residual W<latexit sha1_base64="5Ws293h2rgw/KfxB4CXiYvInwmo=">AAACCHicbVDLSsNAFJ34rPUVdenCwSIIQkmqoMuiG5cV7AOaUCbTm3bo5OHMRCghSzf+ihsXirj1E9z5N07aCNp64MLhnHu59x4v5kwqy/oyFhaXlldWS2vl9Y3NrW1zZ7clo0RQaNKIR6LjEQmchdBUTHHoxAJI4HFoe6Or3G/fg5AsCm/VOAY3IIOQ+YwSpaWeeeAERA09P21n2JF3CRGAT/CP6GU9s2JVrQnwPLELUkEFGj3z0+lHNAkgVJQTKbu2FSs3JUIxyiErO4mEmNARGUBX05AEIN108kiGj7TSx34kdIUKT9TfEykJpBwHnu7ML5SzXi7+53UT5V+4KQvjREFIp4v8hGMV4TwV3GcCqOJjTQgVTN+K6ZAIQpXOrqxDsGdfnietWtU+rdZuzir1yyKOEtpHh+gY2egc1dE1aqAmougBPaEX9Go8Gs/Gm/E+bV0wipk99AfGxzd9p5mi</latexit> ⇤+b

f_A^L

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Residual h^l_u

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W⇤

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W⇤

(W⇤+b)

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m^l_uv

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AO→AO Attention

e^aux_uv

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Residual AO→Atom

Attention

·

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W⇤+b

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Softmax

X A

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f_A^l

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h^l+1_u

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e^l+1_uv

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Orbitals Atoms

Molecule

Figure 2.6: Detail of a single message-passing and pooling layer (“Message Passing Layer” in Fig. 2.2), and a decoding network (“Decoding” in Fig. 2.2). At message passing and pooling layer𝑙+1, the whole-molecule, atom-specific, node-specific, and edge-specific attributes are updated. The atom-specific attributesf^𝑙_𝐴are updated with input from node- and edge-specific attributesh𝑢^𝑙 ande^𝑙𝑢𝑣 and likewise includes the back-propagation from the whole-molecule attributes; finally, the whole-molecule attributes q^𝑙 are updated with input from the atom-specific attributes. The final atom-specific attributes are passed into separate decoding networks to generate the energy prediction and auxiliary target predictions. A decoding network is composed of multiple residual blocks (“Residual”) and a linear output layer, as illustrated above.

diverse dataset of drug-like molecules, as compiled by Folmsbee and Hutchison,[64]

it is shown that OrbNet provides a prediction accuracy that is similar to DFT and much improved over existing ML methods, but at a computational cost that is reduced by at least three orders of magnitude relative to DFT. Natural future directions for development will include the expansion of OrbNet to a broader set of chemical elements, incorporation of directional message-passing and model supervision using prior physical information,[52–54] and end-to-end refitting of the semi-empirical method used for feature generation.[33, 77]

Dalam dokumen Physics-Informed Neural Approaches for Multiscale Molecular Modeling and Design (Halaman 41-44)