Learning Structural Eigenmodes with Modal Operator Network (ModalONet)

What the math gives to ML

The paper provides a transferable modal-factorization mechanism rather than merely applying a standard neural operator: a spatial trunk learns continuous basis functions, while a pole-residue temporal branch learns modal coordinates whose poles directly encode frequencies and damping. The reconstruction, orthonormality, and temporal projection-consistency losses create an identifiable latent representation without labeled eigenmodes. This can be transferred to spatiotemporal forecasting by replacing an unconstrained latent state-space bottleneck with a stable modal bottleneck, yielding interpretable modes and explicit long-horizon stability conditions through the learned poles.