Related papers: Frequency-Separable Hamiltonian Neural Network for…

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…

In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…

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…

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…

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule $x_t = x_t^{(\mathrm{ex})}…

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…

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…

Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…

Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To…

The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…

Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing…

We consider the learning and prediction of nonlinear time series generated by a latent symplectic map. A special case is (not necessarily separable) Hamiltonian systems, whose solution flows give such symplectic maps. For this special case,…

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…