SparseModesNet uses linear POD encoding plus LassoNet-enforced sparse nonlinear neural decoding to select informative modes and cut reconstruction error on advection-dominated and turbulent flows.
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FastQM rotates a candidate basis of singular vectors on the Stiefel manifold to maximize quadratic manifold approximation quality, with feature-space cost independent of full dimension, shown on turbulent airfoil-wake data.
A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.
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Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
SparseModesNet uses linear POD encoding plus LassoNet-enforced sparse nonlinear neural decoding to select informative modes and cut reconstruction error on advection-dominated and turbulent flows.