Related papers: Deep Learning based discovery of Integrable System…
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…
In most works on deep incremental learning research, it is assumed that novel samples are pre-identified for neural network retraining. However, practical deep classifiers often misidentify these samples, leading to erroneous predictions.…
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in…
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As…
We construct an extended Hubbard model with open boundaries from a $R$-matrix based on the $U_q[Osp(2|2)]$ superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open…
We explore the algebraic structure of a particular ansatz of Yang Baxter Equation which is inspired from the Bethe Ansatz treatment of the ASEP spin-model. Various classes of Hamiltonian density arriving from two types of R-Matrices are…
This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…
In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to classify constant Yang-Baxter solutions for a two-dimensional…
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
We refine the recently introduced notion of eclectic spin chains by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians.…
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…