# FCHL revisited: faster and more accurate quantum machine learning Source: [FCHL revisited: faster and more accurate quantum machine learning]() Collection index: [llms.txt]() Data updated: 2025-10-25T00:36:56.520Z Authors: Anders S. Christensen, Lars A. Bratholm, Felix A. Faber, O. Anatole von Lilienfeld Published: 2019-09-04T17:17:20.000Z ## Abstract We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical accuracy on the scale of milliseconds. FCHL19 is a revision of our previous work \[Faber et al. 2018\] where the representation is discretized and the individual features are rigorously optimized using Monte Carlo optimization. Combined with a Gaussian kernel function that incorporates elemental screening, chemical accuracy is reached for energy learning on the QM7b and QM9 datasets after training for minutes and hours, respectively. The model also shows good performance for non-bonded interactions in the condensed phase for a set of water clusters with an MAE binding energy error of less than 0.1 kcal/mol/molecule after training on 3,200 samples. For force learning on the MD17 dataset, our optimized model similarly displays state-of-the-art accuracy with a regressor based on Gaussian process regression. When the revised FCHL19 representation is combined with the operator quantum machine learning regressor, forces and energies can be predicted in only a few milliseconds per atom. The model presented herein is fast and lightweight enough for use in general chemistry problems as well as molecular dynamics simulations. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Force Prediction on MD17 Ethanol](): Force Prediction; MD17 Ethanol; MAE (kcal/mol/Å): 0.136. - [Force Prediction on MD17 Uracil](): Force Prediction; MD17 Uracil; MAE (kcal/mol/Å): 0.105. - [Energy Prediction on MD17 Uracil](): Energy Prediction; MD17 Uracil; MAE (kcal/mol): 0.104. - [Energy Prediction on MD17 Salicylic acid](): Energy Prediction; MD17 Salicylic acid; MAE (kcal/mol): 0.114. - [Energy Prediction on MD17 Toluene](): Energy Prediction; MD17 Toluene; MAE (kcal/mol): 0.098. - [Energy Prediction on MD17 Naphthalene](): Energy Prediction; MD17 Naphthalene; MAE (kcal/mol): 0.117. - [Energy Prediction on MD17 Aspirin](): Energy Prediction; MD17 Aspirin; MAE (kcal/mol): 0.182. - [Force Prediction on MD17 Aspirin](): Force Prediction; MD17 Aspirin; MAE (kcal/mol/Å): 0.478. - [Energy Prediction on MD17 Malonaldehyde](): Energy Prediction; MD17 Malonaldehyde; MAE (kcal/mol): 0.081. - [Force Prediction on MD17 Malonaldehyde](): Force Prediction; MD17 Malonaldehyde; MAE (kcal/mol/Å): 0.245. - [Energy Prediction on MD17 Ethanol](): Energy Prediction; MD17 Ethanol; MAE (kcal/mol): 0.054. - [Force Prediction on MD17 Naphthalene](): Force Prediction; MD17 Naphthalene; MAE (kcal/mol/Å): 0.151. - [Force Prediction on MD17 Salicylic acid](): Force Prediction; MD17 Salicylic acid; MAE (kcal/mol/Å): 0.221. - [Force Prediction on MD17 Toluene](): Force Prediction; MD17 Toluene; MAE (kcal/mol/Å): 0.203. - [Molecular Property Prediction on QM9 (test)](): Molecular property prediction; QM9 (test); mu: not recorded. - [Energy and Force Prediction on MD17](): Energy and force prediction; MD17; Average Force Error (kcal/mol/Å): not recorded. ## Original sources and implementation [Original paper]() [PDF]()