ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost

ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost Justin S. Smith Olexandr Isayev Adrián E. Roitberg

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ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost 2017 Chemical Science 10.1039/c6sc05720a smith2017-ani-1-an-extensible-neural-network smith2017-ani-1-an-extensible-neural-network.txt, the project's staged copy 4e4dbaa750fdba5637eb557031cab47026891285 cc-by-nc materials-science

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them transferable atomistic potentials for organic molecules - whether a network trained on quantum-mechanical energies for small molecules can predict energies for larger ones it never saw Quotation withheld because this record is not cleared for redistribution. whether the accuracy-for-speed trade that empirical potentials have always made can be avoided, rather than merely moved Quotation withheld because this record is not cleared for redistribution. the ANI method - atomic environment vectors from modified Behler-Parrinello symmetry functions, plus Normal Mode Sampling - and ANI-1, a potential trained on 17.2 million DFT conformations of molecules up to 8 heavy atoms Quotation withheld because this record is not cleared for redistribution. method Quotation withheld because this record is not cleared for redistribution. transferability - a fitted potential's ability to hold outside the domain it was fitted in, which this field has no systematic way to estimate Quotation withheld because this record is not cleared for redistribution. system-or-tool-building system-or-tool-building Quotation withheld because this record is not cleared for redistribution. a sorted coulomb matrix sized for the largest training molecule leaves elements that are constant zero throughout training; a larger test molecule makes those elements non-zero, feeding values into network parameters that were never updated, so the output is arbitrary rather than merely inaccurate untrained parameters reached only by larger inputs Quotation withheld because this record is not cleared for redistribution. symmetry functions that sum over all neighbours identically leave the network unable to tell a carbon from a hydrogen at a given distance, so the same vector element means different things in different molecules and training cannot resolve it atom-type indistinguishability blocking learning Quotation withheld because this record is not cleared for redistribution. MD follows one well-defined path across the potential surface, so a data set built from it is a sample of that path rather than of the surface; overcoming the bias requires a trajectory long enough to lose its own starting point trajectory bias in molecular-dynamics sampling Quotation withheld because this record is not cleared for redistribution. normal mode sampling can miss interactions in any single molecule, but a data set of many molecules contains the same interaction in other contexts - so accuracy depends on the number of distinct molecules and not only on points per molecule cross-molecule overlap covering a sampler's gaps Quotation withheld because this record is not cleared for redistribution. the headline 0.6 kcal/mol holds only within 30 kcal/mol of each molecule's energy minimum; across the whole sampled range the RMSE is 1.8 Quotation withheld because this record is not cleared for redistribution. the potential covers only H, C, N and O, and only near-equilibrium conformations, because full sampling of each structure's potential surface is near intractable Quotation withheld because this record is not cleared for redistribution. Normal Mode Sampling is stated by the authors to be simply an approximation for generating structures, not a sampling of the true potential surface Quotation withheld because this record is not cleared for redistribution. its accuracy is a property of the training data rather than of the method - the authors say so, and make the improvement path more data rather than a better model Quotation withheld because this record is not cleared for redistribution. the error had not plateaued at the largest data set built, so the reported accuracy is a point on a curve still moving rather than a converged property Quotation withheld because this record is not cleared for redistribution. deep learning architectures and their training machinery - mini-batches, ADAM, max-norm regularisation, early stopping - carried from image and speech recognition into quantum chemistry Quotation withheld because this record is not cleared for redistribution. normal mode analysis, carried from vibrational spectroscopy into a sampler for generating training conformations Quotation withheld because this record is not cleared for redistribution. testing only on molecules LARGER than any in the training set - every case study uses more than eight heavy atoms, where training stopped at eight eliminates: an accuracy that holds only inside the size range the network was trained on · outcome: held Quotation withheld because this record is not cleared for redistribution. two baselines carried through the same training - a coulomb-matrix MLP, and an ANI network with atom types NOT differentiated - so the contribution of each design choice is separable eliminates: the whole architecture being credited with a gain that the representation or one design choice supplies · outcome: held Quotation withheld because this record is not cleared for redistribution. comparison against three incumbent semi-empirical methods, DFTB, PM6 and AM1, on every case study rather than against DFT alone eliminates: a neural potential compared only against the reference it was trained to imitate, and never against the methods it is meant to replace · outcome: held Quotation withheld because this record is not cleared for redistribution. checking that the potential surface is SMOOTH and not merely low-error, because a potential with the right energies and the wrong curvature is useless for dynamics eliminates: a potential with the right energies and the wrong curvature passing as usable for molecular dynamics · outcome: held Quotation withheld because this record is not cleared for redistribution. training-set size varied to check whether accuracy had converged, rather than reporting the largest run alone eliminates: an accuracy figure reported from the largest training run without showing whether it had converged · outcome: partial Quotation withheld because this record is not cleared for redistribution. transferability transferability Quotation withheld because this record is not cleared for redistribution. ANI-1 ANI-1 Quotation withheld because this record is not cleared for redistribution. baseline 1 baseline 1 Quotation withheld because this record is not cleared for redistribution. NMS NMS Quotation withheld because this record is not cleared for redistribution. ReaxFF ReaxFF Quotation withheld because this record is not cleared for redistribution. SFs SFs Quotation withheld because this record is not cleared for redistribution. DTNN DTNN Quotation withheld because this record is not cleared for redistribution. coulomb matrices coulomb matrices Quotation withheld because this record is not cleared for redistribution. overtraining overtraining Quotation withheld because this record is not cleared for redistribution. network architecture network architecture Quotation withheld because this record is not cleared for redistribution. cost function cost function Quotation withheld because this record is not cleared for redistribution. semi-empirical methods semi-empirical methods Quotation withheld because this record is not cleared for redistribution. RMSE of ANI-1 against DFT - OVER THE WHOLE SAMPLING: 1.8 kcal/mol across 8,245 conformations of 134 ten-heavy-atom molecules Quotation withheld because this record is not cleared for redistribution. RMSE of ANI-1 against DFT - WITHIN 30 kcal/mol OF THE MINIMUM: 0.6 kcal/mol. The number the conclusion quotes, and the window is stated with it Quotation withheld because this record is not cleared for redistribution. the better model - ON THE ANI-1 TEST SET: the two baselines perform better than ANI-1 Quotation withheld because this record is not cleared for redistribution. the better model - ON THE GDB-10 EXTENSIBILITY SET: ANI-1 at 1.9 kcal/mol against baseline 1 at 493.7. Same models, same training, opposite ranking, and the disambiguator is whether the test molecules are larger than the training ones Quotation withheld because this record is not cleared for redistribution. extends → Behler and Parrinello's symmetry-function representation, by adding angular shifts and atomic-number differentiation to make it transferable across chemical environments Quotation withheld because this record is not cleared for redistribution. critiques → empirical and semi-empirical potentials, which trade accuracy for speed and offer no systematic way to estimate their own transferability Quotation withheld because this record is not cleared for redistribution. qualifies → neural network potentials demonstrated on single systems or short molecular-dynamics trajectories, which were never shown to predict energies for larger molecules Quotation withheld because this record is not cleared for redistribution. ANI-1 —contrasted-with→ baseline 1 ANI-1 baseline 1 differs in: total energy RMSE on the GDB-10 extensibility set - 1.9 against 493.7 kcal/mol · the relation itself is separately evidenced · strength of the relation: 0.95 · differs in (stated by the tagger, no quotation): total energy RMSE on the GDB-10 extensibility set - 1.9 against 493.7 kcal/mol · the relation stated: ANI-1 extends to larger molecules and the coulomb-matrix baseline does not Quotation withheld because this record is not cleared for redistribution. network architecture —causes→ overtraining network architecture overtraining direction on the measure: increases · the relation itself is separately evidenced · strength of the relation: 0.8 · direction on the measure (stated by the tagger, no quotation): increases · the relation stated: too large a network generalises badly across structures because it overtrains Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says too large a network can lead to overtraining; the sign holds for size, not architecture. Quotation withheld because this record is not cleared for redistribution. ANI-1 is chemically accurate against DFT on molecules up to 54 atoms, much larger than those in its training set. ANI-1 is chemically accurate against DFT on molecules up to 54 atoms, much larger than those in its training set. Quotation withheld because this record is not cleared for redistribution. the RMSE is 1.8 kcal/mol over the whole sampling and 0.6 within 30 kcal/mol of the minimum - the same model under two windows the RMSE is 1.8 kcal/mol over the whole sampling and 0.6 within 30 kcal/mol of the minimum - the same model under two windows Quotation withheld because this record is not cleared for redistribution. The baselines do better on the ANI-1 test set but fail to extend to the larger GDB-10 molecules. The baselines do better on the ANI-1 test set but fail to extend to the larger GDB-10 molecules. Quotation withheld because this record is not cleared for redistribution. Baseline 1 fails on larger molecules because coulomb-matrix elements that stayed zero in training become non-zero and feed untrained parameters. Baseline 1 fails on larger molecules because coulomb-matrix elements that stayed zero in training become non-zero and feed untrained parameters. Quotation withheld because this record is not cleared for redistribution. there are no systematic ways for improving or estimating the transferability of empirical potentials there are no systematic ways for improving or estimating the transferability of empirical potentials Quotation withheld because this record is not cleared for redistribution. Extensibility increases with data set size and had not plateaued at the current size. Extensibility increases with data set size and had not plateaued at the current size. Quotation withheld because this record is not cleared for redistribution. whether a potential holds outside the systems it was parameterised on; ReaxFF is given as the counter-case, being reparameterised system to system and so lacking an out-of-the-box level of it transferability Quotation withheld because this record is not cleared for redistribution. Normal Mode Sampling - perturbing an energy-minimised structure along its normal modes to a chosen maximum energy, explicitly an approximation for generating structures NMS Quotation withheld because this record is not cleared for redistribution. ANI-1's RMSE against DFT over the entire random sampling 1.8 kcal mol–1 Quotation withheld because this record is not cleared for redistribution. the energy window within which the RMSE falls to 0.6 - the restriction the headline number carries 30.0 kcal mol–1 Quotation withheld because this record is not cleared for redistribution. baseline 1's total-energy RMSE on the extensibility set, against ANI-1's 1.9 493.7 kcal mol–1 Quotation withheld because this record is not cleared for redistribution. RMSE RMSE Quotation withheld because this record is not cleared for redistribution. root mean squared error root mean squared error Quotation withheld because this record is not cleared for redistribution. network architecture network architecture Quotation withheld because this record is not cleared for redistribution.

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