Related papers: Machine Learned H\"uckel Theory: Interfacing Physi…

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…

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous works focuses on generating predictions for…

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…

Neural mass models describe the mean-field dynamics of populations of neurons. In this work we illustrate how fundamental ideas of physics, such as energy and conserved quantities, can be explored for such models. We show that…

Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…

Traditional atomistic machine learning (ML) models serve as surrogates for quantum mechanical (QM) properties, predicting quantities such as dipole moments and polarizabilities, directly from compositions and geometries of atomic…

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a…

The effective spin Hamiltonian method is widely adopted to simulate and understand the behavior of magnetism. However, the magnetic interactions of some systems, such as itinerant magnets, are too complex to be described by any explicit…

We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical…

We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…

We introduce QERNEL, a foundational neural wavefunction that variationally solves families of parameterized many-electron Hamiltonians and captures their ground states throughout parameter space within a single model. QERNEL combines…

We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…

These lecture notes introduce some simple effective Hamiltonians (also known as semi-empirical models) that have widespread applications to solid state and molecular systems. They are aimed as an introduction to a beginning graduate…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…

A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are…

DFT+U is a widely used treatment in the density functional theory (DFT) to deal with correlated materials that contain open-shell elements, whereby the quantitative and sometimes even qualitative failures of local and semilocal…

H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based…

We develop a neural network model, based on the processes of high-energy heavy-ion collisions, to study and predict several experimental observables in Au+Au collisions. We present a data-driven deep learning framework for predicting…