Fast and Accurate Uncertainty Estimation in Chemical Machine Learning

Musil, Félix; Willatt, Michael J.; Langovoy, Mikhail A.; Ceriotti, Michele

doi:10.1021/acs.jctc.8b00959

Cited by 137 publications

(142 citation statements)

References 57 publications

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“…The SOAP-GPR framework is robust, easily trained, has recently been generalised to the prediction of tensorial properties such as (anisotropic) chemical shielding tensors [70]. Furthermore, it provides accurate estimates of prediction uncertainty [67]. These are particularly important in this context, not only to estimate the reliability of assignments, but also because GIPAW calculations can at times yield unreliable results, and the ML model can be improved by automatically discarding problematic training data (see appendix A).…”

Section: Methodsmentioning

confidence: 99%

A Bayesian approach to NMR crystal structure determination

Engel

Anelli

Hofstetter

et al. 2019

Phys. Chem. Chem. Phys.

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Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well-suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical error in the electronic structure methods. We also extend the recently-developed ShiftML machine-learning model, including the evaluation of the uncertainty of its predictions. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the of similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated 13 C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use 13 C shifts to improve the accuracy of structure determinations.

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Section: Methodsmentioning

confidence: 99%

A Bayesian approach to NMR crystal structure determination

Engel

Anelli

Hofstetter

et al. 2019

Phys. Chem. Chem. Phys.

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“…where I and J run over the training structures. As detailed in [40], this strategy is however not very practical because of its computational expense, so that other kind of methods such as bootstrapping or subsampling can rather be used to estimate the prediction errors. In addition, in the particular case of the present work one would like to propagate the error that occurs in the prediction of a to the Raman spectrum.…”

Section: Errors and Uncertainty Estimationsmentioning

confidence: 99%

“…This is of course not true in general, so that one needs to correct the model to take into account for the underlying correlations. Following [40], a maximum likelihood recipe can be adopted to linearly scale the variance of the predictions by a constant factor ν 2 . The calibration of this scaling factor is carried out by computing the actual prediction errors of the polarizabilites over a suitably selected validation set N val , for which the reference polarizabilities are known, and then considering where σ 2 ( j) are the variances of the predicted polarizabilities.…”

Section: Errors and Uncertainty Estimationsmentioning

confidence: 99%

Using Gaussian process regression to simulate the vibrational Raman spectra of molecular crystals

et al. 2019

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Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very costly, especially when dealing with response properties of materials to e.g. electric fields, which require a good description of the perturbed electronic density. In this work, we use Gaussian process regression (GPR) to predict the static polarizability and dielectric susceptibility of molecules and molecular crystals. We combine this framework with ab initio molecular dynamics to predict their anharmonic vibrational Raman spectra. We stress the importance of data representation, symmetry, and locality, by comparing the performance of different flavors of GPR. In particular, we show the advantages of using a recently developed symmetry-adapted version of GPR. As an examplary application, we choose Paracetamol as an isolated molecule and in different crystal forms. We obtain accurate vibrational Raman spectra in all cases with fewer than 1000 training points, and obtain improvements when using a GPR trained on the molecular monomer as a baseline for the crystal GPR models. Finally, we show that our methodology is transferable across polymorphic forms: we can train the model on data for one crystal structure, and still be able to accurately predict the spectrum for a second polymorph. This procedure provides an independent route to access electronic structure properties when performing force-evaluations on empirical force-fields or machine-learned potential energy surfaces.

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“…Their scheme is based on resampling wherein they generate multiple models based on subsampling of the same training data. They benchmark the accuracy of the uncertainty prediction by maximum likelihood estimation which in turn can correct for correlations between resampled models and improve performance of the uncertainty estimation via a cross-validation procedure [120]. By tracking model uncertainty during the MD simulation, a call to the high-fidelity (but expensive) DFT calculation can made when the system drifts to a configuration where the model is uncertain in the energy/force prediction beyond a certain threshold [102,121,122].…”

Section: Iterative Improvement Of Ff Using Active and Transfer Learningmentioning

confidence: 99%

Machine learning for multi-fidelity scale bridging and dynamical simulations of materials

Batra

Sankaranarayanan

2020

J. Phys. Mater.

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Molecular dynamics (MD) is a powerful and popular tool for understanding the dynamical evolution of materials at the nano and mesoscopic scales. There are various flavors of MD ranging from the high fidelity albeit computationally expensive ab-initio MD to relatively lower fidelity but much more efficient classical MD such as atomistic and coarse-grained models. Each of these different flavors of MD have been independently used by materials scientists to bring about breakthroughs in materials discovery and design. A significant gulf exists between the various MD flavors, each having varying levels of fidelity. The accuracy of DFT or ab-initio MD is generally much higher than that of classical atomistic simulations which is higher than that of coarse-grained models. Multi-fidelity scale bridging to combine the accuracy and flexibility of ab-initio MD with efficiency classical MD has been a longstanding goal. The advent of big-data analytics has brought to the forefront powerful machine learning methods that can be deployed to achieve this goal. Here, we provide our perspective on the challenges in multi-fidelity scale bridging and trace the developments leading up to the use of machine learning algorithms and data-science towards addressing this grand challenge. arXiv:2004.00232v1 [physics.comp-ph] 1 Apr 2020

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Fast and Accurate Uncertainty Estimation in Chemical Machine Learning

Cited by 137 publications

References 57 publications

A Bayesian approach to NMR crystal structure determination

A Bayesian approach to NMR crystal structure determination

Using Gaussian process regression to simulate the vibrational Raman spectra of molecular crystals

Machine learning for multi-fidelity scale bridging and dynamical simulations of materials

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