In this work, we demonstrate how physical principles—such as symmetries, invariances and
conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is …

Point clouds are versatile representations of 3D objects and have found widespread
application in science and engineering. Many successful deep-learning models have been …

Research in modern data-driven dynamical systems is typically focused on the three key
challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode …

The quantum many-body problem is ultimately a curse of dimensionality: the state of a
system with many particles is determined by a function with many dimensions, which rapidly …

The application of quantum computation to accelerate machine learning algorithms is one of
the most promising areas of research in quantum algorithms. In this paper, we explore the …

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate
data can be highly expensive. Here, machine learning (ML) models can help to be data …

Koopman operator theory has been successfully applied to problems from various research
areas such as fluid dynamics, molecular dynamics, climate science, engineering, and …

We consider universal approximations of symmetric and anti-symmetric functions, which are
important for applications in quantum physics, as well as other scientific and engineering …

This work introduces a new permutation-symmetry-adapted machine learning diabatization
procedure, termed the diabatization by equivariant neural network (DENN). In this approach …

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic
potential of a molecule from its electron density dynamics. Although the entire TDHF …