arXiv subjects

O. A. von Lilienfeld

Publications and source records attributed to O. A. von Lilienfeld.

4 recordsLinked to original sources

arXiv2026

Gradient-Guided Furthest Point Sampling for Robust Training Set Selection

Training set sampling methods are used to improve model performance and lower data costs in machine learning problems relevant to chemistry. We introduce Gradient Guided Furthest Point Sampling (GGFPS), a simple extension of Furthest Point Sampling (FPS) that leverages molecular force norms to guide efficient sampling of configurational spaces of molecules. Numerical evidence is presented for a toy system (the Styblinski-Tang function) as well as for molecular dynamics trajectories from the MD17 dataset. Our numerical results indicate superior data efficiency and model robustness when using GGFPS compared to FPS and uniform random sampling (URS), as well as established supervised FPS-style selectors, PCov-FPS and PCov-CUR. Distribution analysis of the MD17 data suggests that FPS systematically under-samples equilibrium geometries, resulting in large test errors for relaxed structures. GGFPS cures this artifact and (i) enables up to twofold reductions in training cost without sacrificing predictive accuracy compared to FPS in the 2-dimensional Styblinski-Tang system, (ii) systematically lowers prediction errors for equilibrium as well as strained structures in MD17, and (iii) systematically decreases prediction error variances across all of the MD17 configuration spaces. These results suggest that gradient-aware sampling methods hold great promise as effective training set selection tools, and that naive use of FPS may result in imbalanced training and inconsistent prediction outcomes.

stat.ML↗

arXiv2022

Geometry Relaxation and Transition State Search throughout Chemical Compound Space with Quantum Machine Learning

We use energies and forces predicted within response operator based quantum machine learning (OQML) to perform geometry optimization and transition state search calculations with legacy optimizers. For randomly sampled initial coordinates of small organic query molecules we report systematic improvement of equilibrium and transition state geometry output as training set sizes increase. Out-of-sample S$_\mathrm{N}$2 reactant complexes and transition state geometries have been predicted using the LBFGS and the QST2 algorithm with an RMSD of 0.16 and 0.4 Å -- after training on up to 200 reactant complexes relaxations and transition state search trajectories from the QMrxn20 data-set, respectively. For geometry optimizations, we have also considered relaxation paths up to 5'500 constitutional isomers with sum formula C$_7$H$_{10}$O$_2$ from the QM9-database. Using the resulting OQML models with an LBFGS optimizer reproduces the minimum geometry with an RMSD of 0.14~Å. For converged equilibrium and transition state geometries subsequent vibrational normal mode frequency analysis indicates deviation from MP2 reference results by on average 14 and 26\,cm$^{-1}$, respectively. While the numerical cost for OQML predictions is negligible in comparison to DFT or MP2, the number of steps until convergence is typically larger in either case. The success rate for reaching convergence, however, improves systematically with training set size, underscoring OQML's potential for universal applicability.

physics.chem-ph↗

arXiv2020

Torsional potentials of glyoxal, oxalyl halides and their thiocarbonyl derivatives: Challenges for popular density functional approximations

The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides and their thiocarbonyl derivatives. HF and \textcolor{black}{eighteen} functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, all functionals except M05-2X and M06-2X fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion corrections show no improvement. Calibrated torsion-corrected atom-centered potentials rectify the shortcomings of PBE and also improve on $σ$-hole based intermolecular binding in dimers and crystals.

physics.chem-ph↗

arXiv2012

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

A well-defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we review an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand-canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via "alchemical" interpolations involving fractional nuclear chargens in the electronic Hamiltonian. We address Taylor expansions in CCS, property non-linearity, improved predictions using reference compound pairs, and the ounce-of-gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schrödinger equation.

physics.chem-ph↗