Learning a Reduced Basis of Dynamical Systems using an Autoencoder

The paper empirically demonstrates that an autoencoder with latent-space L1 penalty (i) finds ~10 active latent coordinates for KS at L=22 with optimal λ≈0.398 and a nonlinear low-wavenumber basis via activation maximization, (ii) selects λ*=0 and shows no active/inactive split for undamped KdV, and (iii) yields a median active-count that decreases nearly monotonically with damping η for damped KdV, with early signs of power-law behavior . The candidate solution reproduces these findings and adds reasonable theoretical motivation (e.g., sparse latent selection, spectral decay for damped KdV) consistent with the empirical results.