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The prediction of product translational, vibrational, and rotational energy distributions for arbitrary initial conditions for reactive atom+diatom collisions is of considerable practical interest in atmospheric re-entry. Due to the large…

We develop a structured theoretical framework used in our recent articles [Eur. Phys. J. B 92, 93 (2019) and Phys. Rev. B 101, 094427 (2020)] to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic…

Biomolecular thermodynamics and spectroscopy depend on relative conformer energies, local curvatures, and collective dipole fluctuations on the potential-energy surface. Conventional molecular mechanics force fields enable large-scale…

In this article we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…

Spectral densities encode essential information about system-environment interactions in open-quantum systems, playing a pivotal role in shaping the system's dynamics. In this work, we leverage machine learning techniques to reconstruct key…

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus…

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity…

Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point…

Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in…

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each…

A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent and polarized elementary electric-field modes. This…

Gauss integral theorems for electric and magnetic fields, Faradays law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are…

Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…

We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…

Accurate short-term solar and wind power predictions play an important role in the planning and operation of power systems. However, the short-term power prediction of renewable energy has always been considered a complex regression…