Related papers: Learning Hamiltonian Dynamics at Scale: A Differen…

Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…

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…

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…

Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…

Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse…

Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to…

We introduce a new strategy designed to help physicists discover hidden laws governing dynamical systems. We propose to use machine learning automatic differentiation libraries to develop hybrid numerical models that combine components…

The accurate modeling of spin-orbit coupling (SOC) effects in diverse complex systems remains a significant challenge due to the high computational demands of density functional theory (DFT) and the limited transferability of existing…

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…

The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

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…

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…

We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic integration with a learned parameterization of the…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…

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…