The paper presents a novel machine learning (ML) approach called gradient-domain machine learning (GDML) for constructing accurate molecular force fields. The method leverages the conservation of energy, a fundamental property of classical and quantum mechanical systems, to build models that are both accurate and conservative. GDML uses a small number of samples from ab initio molecular dynamics (AIMD) trajectories to reproduce global potential energy surfaces (PESs) with high precision. Specifically, the approach achieves an accuracy of 0.3 kcal mol\(^{-1}\) for energies and 1 kcal mol\(^{-1}\) Å\(^{-1}\) for atomic forces using only 1000 conformational geometries for training. The authors demonstrate the effectiveness of GDML by applying it to various molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin, showing that it can accurately predict thermodynamic observables using path-integral MD (PIMD). The GDML approach not only reduces the computational cost compared to explicit AIMD simulations but also ensures the consistency between energies and forces, making it suitable for efficient and precise molecular dynamics simulations.The paper presents a novel machine learning (ML) approach called gradient-domain machine learning (GDML) for constructing accurate molecular force fields. The method leverages the conservation of energy, a fundamental property of classical and quantum mechanical systems, to build models that are both accurate and conservative. GDML uses a small number of samples from ab initio molecular dynamics (AIMD) trajectories to reproduce global potential energy surfaces (PESs) with high precision. Specifically, the approach achieves an accuracy of 0.3 kcal mol\(^{-1}\) for energies and 1 kcal mol\(^{-1}\) Å\(^{-1}\) for atomic forces using only 1000 conformational geometries for training. The authors demonstrate the effectiveness of GDML by applying it to various molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin, showing that it can accurately predict thermodynamic observables using path-integral MD (PIMD). The GDML approach not only reduces the computational cost compared to explicit AIMD simulations but also ensures the consistency between energies and forces, making it suitable for efficient and precise molecular dynamics simulations.