Related papers: Finding discrete symmetry groups via Machine Learn…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
An unconventional magnet may be mapped onto a simple ferromagnet by the existence of a high-symmetry point. Knowledge of conventional ferromagnetic systems may then be carried over to provide insight into more complex orders. Here we…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Machine Learning algorithms are good tools for both classification and prediction purposes. These algorithms can further be used for scientific discoveries from the enormous data being collected in our era. We present ways of discovering…
Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…
Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial…
Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…
This paper addresses the task of set prediction using deep learning. This is important because the output of many computer vision tasks, including image tagging and object detection, are naturally expressed as sets of entities rather than…
Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…
Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
We demonstrate a machine learning approach designed to extract hidden chemistry/physics to facilitate new materials discovery. In particular, we propose a novel method for learning latent knowledge from material structure data in which…
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the…
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the…
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…