Related papers: Deep Learning based discovery of Integrable System…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

In this study, we introduce an autonomous method for addressing the detection and classification of quantum entanglement, a core element of quantum mechanics that has yet to be fully understood. We employ a multi-layer perceptron to…

A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order \lambda^6. As an example the classification of 4x4 R-matrices is…

We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…

Artificial Intelligence (AI) systems have shown good success at classifying. However, the lack of explainability is a true and significant challenge, especially in high-stakes domains, such as health and finance, where understanding is…

Autoencoders offer a general way of learning low-dimensional, non-linear representations from data without labels. This is achieved without making any particular assumptions about the data type or other domain knowledge. The generality and…

The increasing use of complex machine learning models in education has led to concerns about their interpretability, which in turn has spurred interest in developing explainability techniques that are both faithful to the model's inner…

An integrable system is introduced, which is a generalization of the $\mathfrak{sl}(2)$ quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within the ODE/IQFT approach. The…

We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…

This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

There are known to be integrable Sutherland models associated to every real root system -- or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper…

We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering…

We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect…

Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability…

Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically…

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…