Related papers: Nonseparable Symplectic Neural Networks

Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress…

Accurate spatial-temporal (ST) prediction for dynamic systems, such as urban mobility and weather patterns, is crucial but hindered by complex ST correlations and the challenge of concurrently modeling long-term trends with short-term…

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the…

An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…

This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…

The predictive learning of spatiotemporal sequences aims to generate future images by learning from the historical context, where the visual dynamics are believed to have modular structures that can be learned with compositional subsystems.…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…

Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…

The nonlinear nature of chaotic systems results in extreme sensitivity to initial conditions and highly intricate dynamical behaviors, posing fundamental challenges for accurately predicting their evolution. To overcome the limitation that…

The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…

Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Probabilistic models and stochastic neural networks can explicitly handle…

Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

This paper develops a helicity-aware physics-informed neural network framework for incompressible non-Newtonian flow in rotational form. In addition to the energy law and the incompressibility constraint, helicity is a fundamental geometric…

The efficiency of modern machine intelligence depends on high accuracy with minimal computational cost. In spiking neural networks (SNNs), synaptic delays are crucial for encoding temporal structure, yet existing models treat them as fully…

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…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we can get the bounds for the perturbation, the variation of…

We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to…