Reduced-Order Models for the Twin

High-dimensional physics fields lie near low-dimensional manifolds; Kronos projects onto the dominant modes to get compact, fast twin components.

Exploiting low-dimensional structure

A temperature or flux field discretized on a fine grid has millions of degrees of freedom, but the family of physically reachable fields is far smaller, most of the variation lives in a handful of modes. Reduced-order modeling finds those dominant modes (via proper orthogonal decomposition or a learned autoencoder latent) and evolves the physics in that compact space, then reconstructs the full field when needed.

# POD-Galerkin style reduced-order model
# snapshots from offline high-fidelity runs -> basis U (r modes)
U = pod_basis(snapshots, rank=r)        # r << full dimension
a = U.T @ field                          # reduced coordinates
a_next = reduced_dynamics(a, u)          # cheap r-dim update
field_hat = U @ a_next                    # reconstruct when needed

The payoff is speed and stability: evolving r modes instead of millions of grid points is cheap and predictable, which suits the shadow's fixed latency budget. Kronos uses reduced-order models where the field is smooth and low-rank, thermal fields, slowly varying equilibria, and reserves full neural operators or PINNs where sharp features (the pedestal, the plug throat) resist low-rank compression.

Guarding reduced models

A reduced model is only valid where its basis spans the true field. If the machine reaches a state whose field has significant energy outside the retained modes, the reconstruction error rises. Kronos monitors that projection residual as a validity check, a rising residual means the reduced model is being asked to represent something outside its basis, and the twin lowers confidence or falls back to a richer surrogate.

Reduced-order latents also serve the anomaly ensemble: an operating point whose reduced coordinates fall outside the training distribution is itself an anomaly signal, complementing the autoencoder-residual detector at the field level.