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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Sirovich, Turbulence and the dynamics of coherent structures
8 Pith papers cite this work, alongside 6,086 external citations. Polarity classification is still indexing.
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RedEigCD enables stable timestep increases up to 40 times larger than full-order models for projection-based ROMs of incompressible flows by using exact spectral bounds on reduced convective and diffusive operators together with a proof that ROM stable timesteps are at least as large as FOM ones.
Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
An iSVD-based adaptive ROM framework updates reduced bases with occasional full-order snapshots, showing improved accuracy and efficiency over direct adaptation baselines on Burgers, Sod, and rotating detonation engine problems.
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.
A framework uses offline-paired LR/HR data and POD latent-space linear models with Kalman filtering to reconstruct high-resolution velocity fields from coarse real-time event-based velocimetry, outperforming cubic interpolation on turbulent jet and ribbed-channel flows.
MF-SHRED maps point-kinetics trajectories to high-fidelity diffusion fields in one LRA benchmark with ~1-2% errors and ~500x speedup, but two of the three claimed benchmarks are absent.
citing papers explorer
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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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Stable self-adaptive timestepping for Reduced Order Models for incompressible flows
RedEigCD enables stable timestep increases up to 40 times larger than full-order models for projection-based ROMs of incompressible flows by using exact spectral bounds on reduced convective and diffusive operators together with a proof that ROM stable timesteps are at least as large as FOM ones.
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Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows
Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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Error bounds for approximate posteriors from likelihood-informed reduced-order models
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
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History-aware adaptive reduced-order models via incremental singular value decomposition
An iSVD-based adaptive ROM framework updates reduced bases with occasional full-order snapshots, showing improved accuracy and efficiency over direct adaptation baselines on Burgers, Sod, and rotating detonation engine problems.
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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.
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Real-Time Estimation of High-Resolution Flow Fields and Reduced-Order Coordinates from Event-Based Imaging Velocimetry
A framework uses offline-paired LR/HR data and POD latent-space linear models with Kalman filtering to reconstruct high-resolution velocity fields from coarse real-time event-based velocimetry, outperforming cubic interpolation on turbulent jet and ribbed-channel flows.
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Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applications
MF-SHRED maps point-kinetics trajectories to high-fidelity diffusion fields in one LRA benchmark with ~1-2% errors and ~500x speedup, but two of the three claimed benchmarks are absent.