Related papers: Dissipative Hamiltonian Neural Networks: Learning …

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…

The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…

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…

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…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

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…

Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work,…

Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to…

In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace…

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…

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…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from…

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…

Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…

Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most…

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian…