Supervise multiple target frames

Use multi-target training to supervise selected intermediate point clouds. A final-frame run passes one (t_rollout - 1, target_pos) pair through the same targets argument, as in Train the emulator from meshes.

Sample the intermediate shapes with waxmorph.data.sample_mesh_sequence(), which accepts (frame, path) pairs, then pass a list of (frame, positions) targets to train:

from waxmorph import TrainConfig, train, chamfer_distance

config = TrainConfig(t_rollout=50, n_epochs=500)

result = train(
    model,
    optimizer,
    chamfer_distance,
    source_pos=source_pos,
    polarities=polarities,
    c=c,
    radii=radii,
    targets=[
        (9, target_pos_early),
        (24, target_pos_mid),
        (49, target_pos_final),
    ],
    config=config,
    device="cuda",
)

Important

Frame k supervises the state after k + 1 complete rollout steps in each model evaluation. Each step includes the learned update and configured mechanics and diffusion. Optimizer updates use the epoch axis; target indices use the within-trajectory frame axis.

Frames must be unique integers in [0, t_rollout); each target must be a nonempty [M, 3] point cloud.

lambda_reg weights sum_t ||dt_gns * GNS_X,t||_F^2, measured after the learned position head and before mechanics. The regularizer covers learned displacement, while the physics update governs prescribed mechanical displacement. Histories contain n_epochs post-update entries; one extra rollout evaluates the final update, and the selected model, loss, and trajectory align.