Dynamically informed nonlinear latent-space representation

Determine how much the inability of the convolutional orthogonal autoencoder representation to support accurate nonlinear emulation would improve when the representation explicitly incorporates the dynamics of the underlying thermosphere.

Background

The paper compares principal component analysis (PCA) and convolutional orthogonal autoencoders (COAE) as dimensionality-reduction methods for the TIEGCM thermospheric density state. Although COAE is intended to represent system nonlinearities more effectively, the COAE–SINDy-AR combination performs slightly worse than the PCA–SINDy-AR combination. The authors attribute this in part to the COAE reduction focusing primarily on reconstruction error within an orthogonal framework, rather than explicitly accounting for the dynamics that the reduced representation must support. The unresolved problem is therefore to determine whether incorporating thermospheric dynamics directly into the latent-space representation can reduce the observed emulation limitations, particularly during geomagnetic storms and other strongly nonlinear regimes.