Hamiltonian neural networks with automatic symmetry detection

Article Mathematics, Applied

Variational learning of Euler-Lagrange dynamics from data

Sina Ober-Bloebaum et al.

Summary: This paper presents the incorporation of variational principles into trajectory predictions of learned dynamical systems. The technique relies on recovering velocities or conjugate momenta using backward error analysis and compensates discretization errors when computing trajectories. The paper also introduces a method for system identification based on variational backward error analysis from position observations only.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2023)

Add to Collection

Article Mathematics, Applied

Symplectic integration of learned Hamiltonian systems

C. Offen et al.

Summary: Hamiltonian systems are differential equations that describe systems in classical mechanics, plasma physics, and sampling problems. Learning the system's Hamiltonian and integrating it with a symplectic integrator improves predictions but requires approximating Hamiltonian data and introduces discretization error. This article introduces a method that directly learns an inverse modified Hamiltonian structure from observations, avoiding the need for approximating Hamiltonian data and eliminating discretization error.

CHAOS (2022)

Add to Collection

Article Instruments & Instrumentation

A bi-stable soft robotic bendable module driven by silicone dielectric elastomer actuators: design, characterization, and parameter study

Matthias Baltes et al.

Summary: This paper presents a novel concept for a planar soft robotic module actuated by smart artificial muscles. The structure can continuously bend along a desired direction through the actuation of antagonist-agonist pair of artificial muscle fibers. Experimental results demonstrate that the bending angle is strongly influenced by the choice of flexible beam geometry and RDEA mounting points, with a maximum bending angle of up to 25 degrees.

SMART MATERIALS AND STRUCTURES (2022)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Learning Motion Primitives Automata for Autonomous Driving Applications

Matheus V. A. Pedrosa et al.

Summary: This paper proposes a method that combines data with a dynamical model to optimally select primitives for motion planning. The method analyzes the data set to identify the most frequently occurring primitives and utilizes Lie group symmetries to design the library, aiming to improve the performance of the motion planner.

MATHEMATICAL AND COMPUTATIONAL APPLICATIONS (2022)

Add to Collection

Article Mathematics, Applied

Symplectic Gaussian process regression of maps in Hamiltonian systems

Katharina Rath et al.

Summary: The approach presented involves constructing structure-preserving emulators for Hamiltonian flow maps and Poincare maps based directly on orbit data. It is intended for moderate-dimensional systems, particularly for long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations. The method utilizes multi-output Gaussian process regression on scattered training data, enforcing the symplectic property through the choice of matrix-valued covariance function for long-term stability.

CHAOS (2021)

Add to Collection

Proceedings Paper Automation & Control Systems

Learning Hamiltonian Systems considering System Symmetries in Neural Networks

Eva Dierkes et al.

Summary: This paper introduces Hamiltonian Neural Networks and their symmetric extensions for learning dynamical systems with Hamiltonian structure. By discussing discrete and continuous symmetries, an improved learning algorithm is proposed to enhance the conservation properties of example systems.

IFAC PAPERSONLINE (2021)

Add to Collection

Article Multidisciplinary Sciences