相关论文: Denoising Hamiltonian Network for Physical Reasoni…

Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…

Identifying the dynamics of physical systems requires a machine learning model that can assimilate observational data, but also incorporate the laws of physics. Neural Networks based on physical principles such as the Hamiltonian or…

There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…

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…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

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…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the…

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…