We present the Electronic Tensor Reconstruction Algorithm (ELECTRA) - an equivariant model for predicting electronic charge densities using "floating" orbitals. Floating orbitals are a long-standing idea in the quantum chemistry community that promises more compact and accurate representations by placing orbitals freely in space, as opposed to centering all orbitals at the position of atoms. Finding ideal placements of these orbitals requires extensive domain knowledge though, which thus far has prevented widespread adoption. We solve this in a data-driven manner by training a Cartesian tensor network to predict orbital positions along with orbital coefficients. This is made possible through a symmetry-breaking mechanism that is used to learn position displacements with lower symmetry than the input molecule while preserving the rotation equivariance of the charge density itself. Inspired by recent successes of Gaussian Splatting in representing densities in space, we are using Gaussians as our orbitals and predict their weights and covariance matrices. Our method achieves a state-of-the-art balance between computational efficiency and predictive accuracy on established benchmarks.

Deep generative models for molecular discovery have become a very popular choice in new high-throughput screening paradigms. These models have been developed inheriting from the advances in natural language processing and computer vision, achieving ever greater results. However, generative molecular modelling has unique challenges that are often overlooked. Chemical validity, interpretability of the generation process and flexibility to variable molecular sizes are among some of the remaining challenges for generative models in computational materials design. In this work, we propose an autoregressive approach that decomposes molecular generation into a sequence of discrete and interpretable steps using molecular fragments as units, a 'molecular story'. Enforcing chemical rules in the stories guarantees the chemical validity of the generated molecules, the discrete sequential steps of a molecular story makes the process transparent improving interpretability, and the autoregressive nature of the approach allows the size of the molecule to be a decision of the model. We demonstrate the validity of the approach in a multi-target inverse design of electroactive organic compounds, focusing on the target properties of solubility, redox potential, and synthetic accessibility. Our results show that the model can effectively bias the generation distribution according to the prompted multi-target objective.

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

Data-driven methods based on machine learning have the potential to accelerate analysis of atomic structures. However, machine learning models can produce overconfident predictions and it is therefore crucial to detect and handle uncertainty carefully. Here, we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. The method presented in this paper differs from the previous work by considering both aleatoric and epistemic uncertainty in a unified framework, and by re-calibrating the predictive distribution on unseen data. Through computer experiments, we show that our approach results in accurate models for predicting molecular formation energies with calibrated uncertainty in and out of the training data distribution on two public molecular benchmark datasets, QM9 and PC9. The proposed method provides a general framework for training and evaluating neural network ensemble models that are able to produce accurate predictions of properties of molecules with calibrated uncertainty.