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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15 Pith papers cite this work, alongside 1,842 external citations. Polarity classification is still indexing.
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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 new symplectic framework and Q-IRKA algorithm achieve H2-optimal model reduction for linear quantum systems while preserving physical realizability by construction.
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.
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
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 WLaSDI-based framework creates noise-robust latent surrogates for PDE-constrained optimization, deriving direct and adjoint gradients to achieve up to five orders of magnitude speedup on radiative transfer, Vlasov-Poisson, and Burgers benchmarks.
New dimension and model reduction techniques for linear Bayesian inverse problems with rank-deficient priors, with approximation guarantees and efficiency demonstrations for high-dimensional inference.
mLaSDI uses multi-stage residual decoder training with periodic activations to recover high-frequency details in latent space dynamics identification, yielding lower reconstruction and prediction errors than standard LaSDI for PDEs.
A latent-space reduced-order model using autoencoders and learned dynamics enables Bayesian recovery of initial density and pressure in Sod shock tube simulations, with posterior uncertainty contracting substantially as observation density increases.
Bayesian-ARGOS is a hybrid frequentist-Bayesian method that discovers equations from limited noisy observations more efficiently than SINDy or bootstrap-ARGOS while adding uncertainty quantification.
Anisotropic Gaussian primitives compress 3D Taylor–Green turbulence at 1e3–1e4× while recovering more intermediate- and high-wavenumber content than isotropic kernels.
A physics-constrained inverse-problem framework identifies graph-based lumped-parameter thermal models from temperature measurements for spacecraft digital-twin applications.
citing papers explorer
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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.
-
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.
-
Symplectic H2 Model Reduction for High-Dimensional Linear Quantum Systems
A new symplectic framework and Q-IRKA algorithm achieve H2-optimal model reduction for linear quantum systems while preserving physical realizability by construction.
-
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.
-
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.
-
Operator Boosting Produces Pareto-Efficient PDE Surrogates
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
-
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.
-
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.
-
Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics
A WLaSDI-based framework creates noise-robust latent surrogates for PDE-constrained optimization, deriving direct and adjoint gradients to achieve up to five orders of magnitude speedup on radiative transfer, Vlasov-Poisson, and Burgers benchmarks.
-
Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances
New dimension and model reduction techniques for linear Bayesian inverse problems with rank-deficient priors, with approximation guarantees and efficiency demonstrations for high-dimensional inference.
-
mLaSDI: Multi-stage latent space dynamics identification
mLaSDI uses multi-stage residual decoder training with periodic activations to recover high-frequency details in latent space dynamics identification, yielding lower reconstruction and prediction errors than standard LaSDI for PDEs.
-
The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows
A latent-space reduced-order model using autoencoders and learned dynamics enables Bayesian recovery of initial density and pressure in Sod shock tube simulations, with posterior uncertainty contracting substantially as observation density increases.
-
Fast and principled equation discovery from chaos to climate
Bayesian-ARGOS is a hybrid frequentist-Bayesian method that discovers equations from limited noisy observations more efficiently than SINDy or bootstrap-ARGOS while adding uncertainty quantification.
-
Gaussian Field Representations for Turbulent Flow: Compression, Scale Separation, and Physical Fidelity
Anisotropic Gaussian primitives compress 3D Taylor–Green turbulence at 1e3–1e4× while recovering more intermediate- and high-wavenumber content than isotropic kernels.
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Physics-constrained identification of graph-based thermal networks for spacecraft digital twins
A physics-constrained inverse-problem framework identifies graph-based lumped-parameter thermal models from temperature measurements for spacecraft digital-twin applications.