Last year, at least 30,000 scientific papers used the Kohn–Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn–Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.

High-throughput density-functional calculations of solids are highly time consuming. As an alternative, we propose a machine learning approach for the fast prediction of solid-state properties. To achieve this, LSDA calculations are used as training set. We focus on predicting the value of the density of electronic states at the Fermi energy. We find that conventional representations of the input data, such as the Coulomb matrix, are not suitable for the training of learning machines in the case of periodic solids. We propose a novel crystal structure representation for which learning and competitive prediction accuracies become possible within an unrestricted class of spd systems of arbitrary unit-cell size.In recent years ab-initio high-throughput computational methods (HTM) have proven to be a powerful and successful tool to predict new materials and to optimize desired materials properties. Phase diagrams of multicomponent crystals [1][2][3] and alloys [4] have been successfully predicted. High-impact technological applications have been achieved by improving the performance of Lithium based batteries [5][6][7], by tailoring the nonlinear optical response in organic molecules [8] for optical signal processing, by designing desired current-voltage characteristics [9] for photovoltaic materials, by optimizing the electrode transparency and conductivity [10] for solar cell technology, and by screening metals for the highest amalgamation enthalpy [11] to efficiently remove Hg pollutants in coal gasification.However, the computational cost of electronic structure calculations poses a serious bottleneck for HTM. Thinking of quaternary, quinternary, etc., compounds, the space of possible materials becomes so large, and the complexity of the unit cells so high that, even within efficient Kohn-Sham density functional theory (KS-DFT), a systematic high-throughput exploration grows beyond reach for present-day computing facilities. As a way out, one would like to have a more direct way to access the physical property of interest without actually solving the KS-DFT equations. Machine learning (ML) techniques offer an attractive possibility of this type. ML-based calculations are very fast, typically requiring only fractions of a second to predict a specific property of a given material, after having trained the ML model on a representative training set of materials.ML methods rely on two main ingredients, the learning algorithm itself and the representation of the input data. There are many different ways of representing a given material or compound. While, from the physicist's point of view, the information is simply given by the charges and the positions of the nuclei, for ML algorithms the specific mathematical form in which this information is given to the machine, is crucial. Roughly speaking, ML algorithms assume a nonlinear map between input data (representing the materials or compounds in our case) and the material-specific property to be predicted. Whether or not a machine can approximate the unknown nonlinear ...

Deployment of modern data-driven machine learning methods, most often realized by deep neural networks (DNNs), in safety-critical applications such as health care, industrial plant control, or autonomous driving is highly challenging due to numerous model-inherent shortcomings. These shortcomings are diverse and range from a lack of generalization over insufficient interpretability and implausible predictions to directed attacks by means of malicious inputs. Cyber-physical systems employing DNNs are therefore likely to suffer from so-called safety concerns, properties that preclude their deployment as no argument or experimental setup can help to assess the remaining risk. In recent years, an abundance of state-of-the-art techniques aiming to address these safety concerns has emerged. This chapter provides a structured and broad overview of them. We first identify categories of insufficiencies to then describe research activities aiming at their detection, quantification, or mitigation. Our work addresses machine learning experts and safety engineers alike: The former ones might profit from the broad range of machine learning topics covered and discussions on limitations of recent methods. The latter ones might gain insights into the specifics of modern machine learning methods. We hope that this contribution fuels discussions on desiderata for machine learning systems and strategies on how to help to advance existing approaches accordingly.