Related papers: Molecular Hessian matrices from a machine learning…

Deep learning models are being adopted and applied on various critical decision-making tasks, yet they are trained to provide point predictions without providing degrees of confidence. The trustworthiness of deep learning models can be…

This thesis designs a prediction system based on matrix factorization to predict the classification accuracy of a specific model on a particular dataset. In this thesis, we conduct comprehensive empirical research on more than fifty…

Despite their importance in a wide variety of applications, the estimation of ionization cross sections for large molecules continues to present challenges for both experiment and theory. Machine learning algorithms have been shown to be an…

Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced…

Quantifying prediction uncertainty when applying object detection models to new, unlabeled datasets is critical in applied machine learning. This study introduces an approach to estimate the performance of deep learning-based object…

In this work, we present a random forest framework that learns the weights, shapes, and sparsities of feature representations for real-time semantic segmentation. Typical filters (kernels) have predetermined shapes and sparsities and learn…

We describe four algorithms for neural network training, each adapted to different scalability constraints. These algorithms are mathematically principled and invariant under a number of transformations in data and network representation,…

This study is devoted to the inference problem of extracting the nuclear matter properties directly from a set of mass-radius observations. We employ Bayesian neural networks (BNNs), which is a probabilistic model capable of estimating the…

The accuracy of any machine learning potential can only be as good as the data used in the fitting process. The most efficient model therefore selects the training data that will yield the highest accuracy compared to the cost of obtaining…

This study proposes a recursive and easy-to-implement algorithm to compute the score and Hessian matrix in general regime-switching models. We use simulation to compare the asymptotic variance estimates constructed from the Hessian matrix…

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…

We review recent studies dealing with the generation of machine learning models of molecular and solid properties. The models are trained and validated using standard quantum chemistry results obtained for organic molecules and materials…

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…

The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…

We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and…

The field of machine learning is subject to an increasing interest in models that are not only accurate but also interpretable and robust, thus allowing their end users to understand and trust AI systems. This paper presents a novel method…

In this work, we discuss use of machine learning techniques for rapid prediction of detonation properties including explosive energy, detonation velocity, and detonation pressure. Further, analysis is applied to individual molecules in…