An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel
developments and relationships with other formalisms. Port-Hamiltonian systems theory …

Thermodynamics could be seen as an expression of physics at a high epistemic level. As
such, its potential as an inductive bias to help machine learning procedures attain accurate …

In this chapter we present a state space interpretation of the small gain and passivity
approach of the previous chapter. Moreover, we will come to some kind of synthesis …

The use of geometric methods in classical mechanics has proven fruitful, with wide
applications in physics and engineering. In this book, Professor Marsden concentrates on …

We present a novel framework for finite element particle-in-cell methods based on the
discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We …

We present an algorithm to learn the relevant latent variables of a large-scale discretized
physical system and predict its time evolution using thermodynamically-consistent deep …

In this article, we present a deep learning method to predict the temporal evolution of
dissipative dynamic systems. We propose using both geometric and thermodynamic …

This updated revision gives a complete and topical overview on Nonconservative Stability
which is essential for many areas of science and technology ranging from particles trapping …

Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the
purpose of explaining structure preserving numerical algorithms. Geometric structures …

This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré)
system by a special dissipation term that has Brockett's double bracket form. We show that a …