Training a Hamiltonian Neural Network (ritog.github.io)

A recent development in the AI/ML landscape has introduced the concept of training a Hamiltonian Neural Network (HNN) to simulate the phase space of a harmonic oscillator. This method diverges from conventional neural network training by employing physics-based derivatives instead of traditional loss calculations. By applying Hamiltonian dynamics, the network learns to predict the Hamiltonian function of the system, thereby providing time derivatives that define the system's trajectory. The article outlines this process using Python and PyTorch, emphasizing the model's training and its ability to accurately simulate physical behaviors such as the oscillation of a weighted pendulum. This advancement is significant for the AI/ML community as it illustrates the potential for neural networks to solve complex scientific problems, leveraging established physical principles. The use of Hamiltonian mechanics can lead to more robust models compared to standard Neural Ordinary Differential Equations (NODEs), thanks to the conservation properties described by Liouville’s Theorem. These properties ensure that the total area of points in phase space is conserved, which enhances the stability and accuracy of the neural network’s predictions. This method not only opens the door to more effective simulations in various scientific fields but also highlights the synergy between physics and AI, showcasing how deep learning can be employed to derive insights from the physical world.