Related papers: Symplectic Neural Networks Based on Dynamical Syst…

Saliency methods generating visual explanatory maps representing the importance of image pixels for model classification is a popular technique for explaining neural network decisions. Hierarchical dynamic masks (HDM), a novel explanatory…

Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…

Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit these symmetries,…

We introduce Graph-Structured Sum-Product Networks (GraphSPNs), a probabilistic approach to structured prediction for problems where dependencies between latent variables are expressed in terms of arbitrary, dynamic graphs. While many…

We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…

Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…

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…

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…

Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…

We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral…

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…

The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…

We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…

The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…

A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…

An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…