For 1D linear advection, a discrete-time sparse full-order model inferred by least squares is guaranteed stable only if the training data satisfy Δt/Δx ≤ (m+1)/(3c), a 'sampling CFL' bound.
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A CFL-type Condition and Theoretical Insights for Discrete-Time Sparse Full-Order Model Inference
For 1D linear advection, a discrete-time sparse full-order model inferred by least squares is guaranteed stable only if the training data satisfy Δt/Δx ≤ (m+1)/(3c), a 'sampling CFL' bound.