A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems | Paper Citation Record

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Digital Twin in manufacturing: A categorical literature review and classification

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Brotzge, Don Berchoff, DaNa L

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Bresch, Daniela I

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Sparse Identifi- cation for bifurcating phenomena in Computational Fluid Dynamics

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Machine Learning-based quadratic closures for non-intrusive Reduced Order Models

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition, 2025

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Koopman-Equivariant Gaussian Processes

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Comparison and combination of reduced-order modelling techniques in 3D parametrized heat transfer problems

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems On latent dynamics learning in nonlinear reduced order modeling

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Model order re- duction assisted by deep neural networks (ROM-net)

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems An artificial neural network framework for reduced order modeling of transient flows

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Williams, Ioannis G

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Nathan Kutz

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This paper cites A Dynamic Mode Decomposition Extension for the Forecasting of Parametric Dynamical Systems.SIAM Journal on Applied Dynamical Systems, 22(3):2432–2458, September 2023.

A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems A Dynamic Mode Decomposition Extension for the Forecasting of Parametric Dynamical Systems.SIAM Journal on Applied Dynamical Systems, 22(3):2432–2458, September 2023

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Brunton, Joshua L

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems On the stability of projection- based model order reduction for convection-dominated laminar and turbulent flows

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Baddoo, Benjamin Herrmann, Beverley J

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Kaptanoglu, Jared L

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Baddoo, Benjamin Herrmann, Beverley J

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Ex- act Inference for Continuous-Time Gaussian Process Dynamics

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Learning unknown ODE models with Gaussian processes

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Scattered Data Approximation

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Learning Stable Nonparametric Dynam- ical Systems with Gaussian Process Regression

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Operator inference for non-intrusive model reduction with quadratic manifolds

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems An analytic comparison of regularization methods for Gaussian Processes

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Extension formulas and norm inequalities in Sobolev Hilbert spaces

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Pedregosa, G

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems PyDMD: Python Dynamic Mode Decomposition

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Ichinaga, Francesco Andreuzzi, Nicola Demo, Marco Tezzele, Karl Lapo, Gianluigi Rozza, Steven L

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems A novel Large Eddy Simula- tion model for the Quasi-Geostrophic equations in a Finite Volume setting

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems ERA5 hourly data on single levels from 1940 to present, 2018

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Consistency of Gaussian Process Regression in Metric Spaces

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Buhmann, and Gerlind Plonka-Hoch

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Behzadan and M

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Fixed Point Theorems and Applications, volume 116 of UNITEXT

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Micchelli, Yuesheng Xu, and Haizhang Zhang

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Fast algorithms for convex quadratic programming and mul- ticommodity flows

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Our case follows by applying the scalar version to every component and by computing theℓ 2 norm

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This paper cites Theorem 1 establishes the core approximation guarantees for the Gaussian process model.

A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Theorem 1 establishes the core approximation guarantees for the Gaussian process model

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems 58, or 59, 57

Reference 59

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 60

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 61

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems 41 We have demonstrated that the GPRODE framework yields a mathematically consistent procedure for inferring dynamical systems from observational data

Reference 62

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 63

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 64

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 65

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 66

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems We have shown convergence of the ODE with derivatives estimated using a finite-difference scheme to the true ODE

Reference 67

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 68

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems Unresolved cited work

Reference 69

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Observation eb95601b-5a83-439c-a19c-3b2d5735df57 · outbound

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A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems We are now ready to prove the convergence of the Forward difference method

Reference 70

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