Machine-learning interatomic potentials (MLPs) are fast, data-driven surrogate models of atomistic systems' potential energy surfaces that can accelerate ab-initio molecular dynamics (MD) simulations by several orders of magnitude. The performance of MLPs is commonly measured as the prediction error in energies and forces on data not used in their training. While low prediction errors on a test set are necessary, they do not guarantee good performance in MD simulations. The latter requires physically motivated performance measures obtained from running accelerated simulations. However, the adoption of such measures has been limited by the effort and domain knowledge required to calculate and interpret them. To overcome this limitation, we present a benchmark that automatically quantifies the performance of MLPs in MD simulations of a liquid-liquid phase transition in hydrogen under pressure, a challenging benchmark system. The benchmark's h-llpt-24 dataset provides reference geometries, energies, forces, and stresses from density functional theory MD simulations at different temperatures and mass densities. The benchmark's Python code automatically runs MLP-accelerated MD simulations and calculates, quantitatively compares and visualizes pressures, stable molecular fractions, diffusion coefficients, and radial distribution functions. Employing this benchmark, we show that several state-of-the-art MLPs fail to reproduce the liquid-liquid phase transition.

Data-driven engineering refers to systematic data collection and processing using machine learning to improve engineering systems. Currently, the implementation of data-driven engineering relies on fundamental data science and software engineering skills. At the same time, model-based engineering is gaining relevance for the engineering of complex systems. In previous work, a model-based engineering approach integrating the formalization of machine learning tasks using the general-purpose modeling language SysML is presented. However, formalized machine learning tasks still require the implementation in a specialized programming languages like Python. Therefore, this work aims to facilitate the implementation of data-driven engineering in practice by extending the previous work of formalizing machine learning tasks by integrating model transformation to generate executable code. The method focuses on the modifiability and maintainability of the model transformation so that extensions and changes to the code generation can be integrated without requiring modifications to the code generator. The presented method is evaluated for feasibility in a case study to predict weather forecasts. Based thereon, quality attributes of model transformations are assessed and discussed. Results demonstrate the flexibility and the simplicity of the method reducing efforts for implementation. Further, the work builds a theoretical basis for standardizing data-driven engineering implementation in practice.

The Green-Kubo (GK) method is a rigorous framework for heat transport simulations in materials. However, it requires an accurate description of the potential-energy surface and carefully converged statistics. Machine-learning potentials can achieve the accuracy of first-principles simulations while allowing to reach well beyond their simulation time and length scales at a fraction of the cost. In this paper, we explain how to apply the GK approach to the recent class of message-passing machine-learning potentials, which iteratively consider semi-local interactions beyond the initial interaction cutoff. We derive an adapted heat flux formulation that can be implemented using automatic differentiation without compromising computational efficiency. The approach is demonstrated and validated by calculating the thermal conductivity of zirconium dioxide across temperatures.

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, including both very small and very large length scales, and the noise-free limit. We show how such features arise in ML models of density functionals.

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densities} are found via a modified Euler-Lagrange constrained minimization of the total energy. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed.

Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly accurate self-consistent densities and molecular forces are found, indicating the possibility for ab-initio molecular dynamics simulations.

The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. Challenges for application of our method to real electronic structure problems are discussed.

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.