Related papers: Dissipative Hamiltonian Neural Networks: Learning …

Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…

Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…

Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our…

Intrinsic image decomposition is the process of separating the reflectance and shading layers of an image, which is a challenging and underdetermined problem. In this paper, we propose to systematically address this problem using a deep…

An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…

Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model…

Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…

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…

Stochastic port-Hamiltonian systems represent open dynamical systems with dissipation, inputs, and stochastic forcing in an energy based form. We introduce stochastic port-Hamiltonian neural networks, SPH-NNs, which parameterize the…

Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…

Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

The H\"uckel Hamiltonian is an incredibly simple tight-binding model famed for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only…

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural…

Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such…

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…