Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol−1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol−1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT  is highlighted by correcting “on the fly” DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

<div> <div> <div> <p>Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal/mol with presently-available functionals. <i>Ab initio </i>methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. We create density functionals from coupled-cluster energies, based only on DFT densities, via machine learning. These functionals attain quantum chemical accuracy (errors below 1 kcal/mol). Moreover, density-based ∆-learning (learning only the correction to a standard DFT calculation, ∆-DFT) significantly reduces the amount of training data required. We demonstrate these concepts for a single water molecule, and then illustrate how to include molecular symmetries with ethanol. Finally, we highlight the robustness of ∆-DFT by correcting DFT simulations of resorcinol on the fly to obtain molecular dynamics (MD) trajectories with coupled-cluster accuracy. Thus ∆-DFT opens the door to running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT is quantitatively incorrect. </p> </div> </div> </div>

It was demonstrated that the interest of a reader can be inferred online from EEG and eye tracking signals, which can potentially be used in novel types of adaptive software, which enrich the interaction by adding implicit information about the interest of the user to the explicit interaction. The study is characterised by the following novelties. Interpretation with respect to the word meaning was necessary in contrast to the usual practice in brain-computer interfacing where stimulus recognition is sufficient. The typical counting task was avoided because it would not be sensible for implicit relevance detection. Several words were displayed at the same time, in contrast to the typical sequences of single stimuli. Neural activity was related with eye tracking to the words, which were scanned without restrictions on the eye movements.

It was demonstrated that BCI methods can extract implicit user-related information in a setting of human-computer interaction. Novelties of the study are the implicit online feedback from EEG and eye tracking, the approximation to a realistic use case in a simulation, and the presentation of a large set of photographies that had to be interpreted with respect to the content.

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art and makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner. We demonstrate the potential of our approach in a transfer learning application, where a model trained on low accuracy reference wavefunctions implicitly learns to correct for electronic many-body interactions from observables computed at a higher level of theory. Such machine-learned wavefunction surrogates pave the way towards novel semi-empirical methods, offering resolution at an electronic level while drastically decreasing computational cost. While we focus on physics * These authors contributed equally.