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We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the…
The answers to many unsolved problems lie in the intractable chemical space of molecules and materials. Machine learning techniques are rapidly growing in popularity as a way to compress and explore chemical space efficiently. One of the…
We have made initial studies of the potential of support vector machines (SVM) for providing statistical models of nuclear systematics with demonstrable predictive power. Using SVM regression and classification procedures, we have created…
We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in…
This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we…
The vibrational behavior of molecules serves as a crucial fingerprint of their structure, chemical state, and surrounding environment. Neutron vibrational spectroscopy provides comprehensive measurements of vibrational modes without…
By adopting a perspective informed by contemporary liquid state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local…
Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate: (i) the…
We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant…
We develop a Machine Learning Inversion method for analyzing scattering functions of mechanically driven polymers and extracting the corresponding feature parameters, which include energy parameters and conformation variables. The polymer…
Despite their rich information content, electronic structure data amassed at high volumes in $ab$ $initio$ molecular dynamics simulations are generally under-utilized. We introduce a transferable high-fidelity neural network representation…
Machine learning in atomistic materials science has grown to become a powerful tool, with most approaches focusing on atomic arrangements, typically decomposed into local atomic environments. This approach, while well-suited for…
Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a…
We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond.…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…