Related papers: Hamiltonian Generative Networks

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks,…

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

In order to make data-driven models of physical systems interpretable and reliable, it is essential to include prior physical knowledge in the modeling framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in deep…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…

Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…

Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource…

Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…

From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…

In traditional Graph Neural Networks (GNNs), the assumption of a fixed embedding manifold often limits their adaptability to diverse graph geometries. Recently, Hamiltonian system-inspired GNNs have been proposed to address the dynamic…

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The…

We propose a novel framework based on neural network that reformulates classical mechanics as an operator learning problem. A machine directly maps a potential function to its corresponding trajectory in phase space without solving the…

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…

Recent advancements in quantum hardware and classical computing simulations have significantly enhanced the accessibility of quantum system data, leading to an increased demand for precise descriptions and predictions of these systems.…

Deep learning techniques for improving fluid flow modelling have gained significant attention in recent years. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the…

Standard neural networks are often overconfident when presented with data outside the training distribution. We introduce HyperGAN, a new generative model for learning a distribution of neural network parameters. HyperGAN does not require…

Neural population activity in cortical and hippocampal circuits can be flexibly reorganized by context, suggesting that cognition relies on dynamic manifolds rather than static representations. However, how such dynamic organization can be…

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we…