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The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational…
Artificial Neural Networks (ANN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions.…
The accurate description of molecule-surface interactions requires a detailed knowledge of the underlying potential-energy surface (PES). Recently, neural networks (NNs) have been shown to be an efficient technique to accurately interpolate…
Atomistic simulations are a powerful tool for studying the dynamics of molecules, proteins, and materials on wide time and length scales. Their reliability and predictiveness, however, depend directly on the accuracy of the underlying…
There has been a veritable explosion of methods and software to perform machine-learned regression on datasets of electronic energies and forces to develop high-dimensional machine learned potential energy surfaces (ML-PESs). A major, but…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They…
We present an efficient approach for generating highly accurate molecular potential energy surfaces (PESs) using self-correcting, kernel ridge regression (KRR) based machine learning (ML). We introduce structure-based sampling to…
Transition intensities for small molecules such as water and CO$_2$ can now be computed with such high accuracy that they are being used to systematically replace measurements in standard databases. These calculations use high accuracy ab…
The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet…
Several pool-based active learning algorithms (AL) were employed to model potential energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be…
We train an equivariant machine learning model to predict energies and forces for a real-world study of hydrogen combustion under conditions of finite temperature and pressure. This challenging case for reactive chemistry illustrates that…
Machine learned chemical potentials have shown great promise as alternatives to conventional computational chemistry methods to represent the potential energy of a given atomic or molecular system as a function of its geometry. However,…
Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
Deep neural networks are gaining in popularity as they are used to generate state-of-the-art results for a variety of computer vision and machine learning applications. At the same time, these networks have grown in depth and complexity in…
The rise of machine learning has greatly influenced the field of computational chemistry, and that of atomistic molecular dynamics simulations in particular. One of its most exciting prospects is the development of accurate,…
Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…