Related papers: Neural Network Approach to Construction of Classic…

In this paper we present a method of constructing a nonlinear accelerator lattice that has an approximate integral of motion that is given upfront. The integral under consideration is a Hamiltonian in normalized (canonical) coordinates that…

Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…

Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…

The majority of computer vision algorithms fail to find higher-order (abstract) patterns in an image so are not robust against adversarial attacks, unlike human lateralized vision. Deep learning considers each input pixel in a homogeneous…

Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs…

Weighting strategy prevails in machine learning. For example, a common approach in robust machine learning is to exert lower weights on samples which are likely to be noisy or quite hard. This study reveals another undiscovered strategy,…

A growing body of work has established the modelling of stochastic processes as a promising area of application for quantum techologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic…

This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

We develop a machine learning algorithm to infer the emergent stochastic equation governing the evolution of an order parameter of a many-body system. We train our neural network to independently learn the directed force acting on the order…

In recent years, advanced deep neural networks have required a large number of parameters for training. Therefore, finding a method to reduce the number of parameters has become crucial for achieving efficient training. This work proposes a…

Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with…

Machine learning-based methods have achieved successful applications in machinery fault diagnosis. However, the main limitation that exists for these methods is that they operate as a black box and are generally not interpretable. This…

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in…

Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…

In this paper, we introduces a Pseudo-Symplectic Neural Network (PSNN) for learning general Hamiltonian systems (both separable and non-separable) from data. To address the limitations of existing structure-preserving methods (e.g.,…

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in…