Introduction
This bi-monthly seminar series explores real-world applications of physics-informed machine learning (Φ-ML) methods to the engineering practice. They cover a wide range of topics, offering a cross-sectional view of the state of the art on Φ-ML research, worldwide.
Participants have the opportunity to hear from leading researchers and learn about the latest developments in this emerging field. These seminars also offer the chance to identify and spark collaboration opportunities.
About the event
Restricting Hamiltonian dynamics to satisfy algebraic constraints is often challenging for traditional numerical algorithms. By leveraging Dirac’s theory of constraints, Hamilton-Dirac neural networks (HDNNs) are introduced as a new class of physics-informed neural networks, capable of learning constrained Hamiltonian dynamics. This parameter-informed machine learning model incorporates Hamilton-Dirac equations, energy conservation, and Dirac constraints through regularization terms in the loss function. As a result, HDNNs accurately predict constrained dynamics while confining system trajectories on the constraint manifold, even in cases where traditional solvers fail. Their effectiveness is demonstrated on systems with holonomic constraints, such as the nonlinear pendulum and a restricted two-dimensional harmonic oscillator, where they outperform conventional solvers in preserving energy and constraints. Additionally, HDNNs are applied to systems with singular Lagrangians, modeling the guiding center motion of a charged particle in a strong magnetic field.
