Related papers: Statistical learning method for predicting density…
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the…
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…
Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical…
Exact expressions for the parameters of Stevens Hamiltonian are derived within the framework of a specific model that assumes uniform character of charge density distribution in a certain direction over crystalline lattice. The new model is…
The H\"uckel Hamiltonian is an incredibly simple tight-binding model famed for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only…
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…
The theorems of density functional theory (DFT) and reduced density matrix functional theory (RDMFT) establish a bijective map between the external potential of a many-body system and its electron density or one-particle reduced density…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…
Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural…
Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…
Dynamical electronic- and vibrational-structure theories have received a growing interest in the last years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular…
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
An efficient algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for…
Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…
Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…
An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…