DeepAI AI Chat
Log In Sign Up

Symplectic integration of learned Hamiltonian systems

by   Christian Offen, et al.

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated.


page 1

page 2

page 3

page 4


Symplecticity of coupled Hamiltonian systems

We derived a condition under which a coupled system consisting of two fi...

Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps

We consider the learning and prediction of nonlinear time series generat...

Variational integration of learned dynamical systems

The principle of least action is one of the most fundamental physical pr...

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian sy...

Hamiltonian Neural Networks

Even though neural networks enjoy widespread use, they still struggle to...

Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

Hamiltonian mechanics is one of the cornerstones of natural sciences. Re...

Learning Trajectories of Hamiltonian Systems with Neural Networks

Modeling of conservative systems with neural networks is an area of acti...

Code Repositories


Accompanying source code to paper "Symplectic integration of learned Hamiltonian systems"

view repo