To extend the physics-constrained machine learning (ML) approach for inferring the full 3D interaction forces in a dusty plasma system, several modifications can be implemented. First, the model architecture should be adapted to include vertical motion by incorporating the z-component of the forces into the neural network structure. This can be achieved by adding additional input parameters that represent the vertical positions of the particles and their corresponding z-accelerations.
The current model primarily focuses on horizontal interactions, which are governed by Newton's second law in the xy-plane. To capture the vertical dynamics, the model can be expanded to include a separate neural network that predicts the vertical forces acting on each particle, taking into account the gravitational forces, electrostatic forces, and the effects of the plasma sheath. This vertical force network could utilize similar input parameters as the horizontal networks but would also need to account for the particle's z-position and the influence of the ion wake on vertical interactions.
Moreover, the training data should include comprehensive 3D trajectory data, ensuring that the model learns from the full range of particle interactions in all three dimensions. By integrating these vertical components into the model, it would be possible to infer the complete interaction forces, providing a more holistic understanding of the dynamics in dusty plasma systems.