A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
Nonlinear Dynamics 41(1--3):309--325
10 Pith papers cite this work, alongside 1,293 external citations. Polarity classification is still indexing.
10
Pith papers citing it
1,293
external citations · OpenAlex
citation-role summary
background 3
citation-polarity summary
roles
background 3polarities
background 3representative citing papers
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
A kernel-based data-driven optimization method computes optimal perturbations to control the spectrum of transfer operators in high-dimensional dynamical systems.
Linear-rate ODE hierarchies can be solved in-window exactly—no boundary cap—by integrating a low-dimensional coefficient ODE and composing generating functions; Strang splitting extends the trick to partially linear-rate models like Schlögl and predator-prey.
Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
Linear response formulas and optimal fingerprinting are extended to nonautonomous reference states, with numerical support from a stochastic Ghil-Sellers energy balance model.
Connects continuum stochastic signals to graphon random walks via Koopman and Perron-Frobenius operators for spectral clustering and graphon reconstruction from data.
Optimizing the activation function in randomized neural networks provides a more suitable dictionary for transfer operator approximation in stochastic differential equations and random walks on graphons.
citing papers explorer
-
Conditional Score-Based Modeling of Effective Langevin Dynamics
A novel identity connects reduced-model drift and diffusion to the conditional score of the finite-time transition density, turning calibration into a least-squares problem over stationary lagged pairs that preserves invariant statistics and dynamical correlations.
-
Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models
Koopman autoencoders with forcings and temporal unrolling deliver accurate year-long predictions for coastal-ocean models at 300-1400x speedup, outperforming POD in two of three cases.
-
Physics-Informed Neural Embeddings of PDE Solution Families
A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.
-
Data-driven methods for computation of optimal linear response in high-dimensional dynamical systems
A kernel-based data-driven optimization method computes optimal perturbations to control the spectrum of transfer operators in high-dimensional dynamical systems.
-
Operator splitting for exploiting linear-rate closure in solving infinite ODE hierarchies
Linear-rate ODE hierarchies can be solved in-window exactly—no boundary cap—by integrating a low-dimensional coefficient ODE and composing generating functions; Strang splitting extends the trick to partially linear-rate models like Schlögl and predator-prey.
-
Controlling Transient Amplification Improves Long-horizon Rollouts
Commutativity regularization mitigates transient error amplification in autoregressive neural simulators by penalizing non-normality and non-commutativity of Jacobians, yielding stable long-horizon rollouts.
-
Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
-
Linear Response and Optimal Fingerprinting for Nonautonomous Systems
Linear response formulas and optimal fingerprinting are extended to nonautonomous reference states, with numerical support from a stochastic Ghil-Sellers energy balance model.
-
Learning graphons from data: Random walks, transfer operators, and spectral clustering
Connects continuum stochastic signals to graphon random walks via Koopman and Perron-Frobenius operators for spectral clustering and graphon reconstruction from data.
-
Optimization of randomized neural networks for transfer operator approximation
Optimizing the activation function in randomized neural networks provides a more suitable dictionary for transfer operator approximation in stochastic differential equations and random walks on graphons.