SparseModesNet uses POD linear encoding with LassoNet-enforced sparse nonlinear NN decoding to select modes and reduce reconstruction error by 51-78% versus polynomial manifold methods on turbulent channel flow while preserving interpretability.
Kernel manifolds: Nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spaces,
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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.
citing papers explorer
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Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
SparseModesNet uses POD linear encoding with LassoNet-enforced sparse nonlinear NN decoding to select modes and reduce reconstruction error by 51-78% versus polynomial manifold methods on turbulent channel flow while preserving interpretability.
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Fast Quadratic Manifold Learning For Nonlinear Dimensionality Reduction in Large-scale Systems using Riemannian Optimization
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.
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A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems
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.