The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
DOI10.1137/21M140691XzbMath1506.65105arXiv2103.11488MaRDI QIDQ5096451
Chao Zhou, Qiang Du, Haizhao Yang, Yiqi Gu
Publication date: 17 August 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.11488
convergence analysislinear multistep methodsLorenz systemdeep learningdata-driven modelingdiscovery of dynamics
Artificial neural networks and deep learning (68T07) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of inverse problems involving ordinary differential equations (65L09)
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Cites Work
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- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- Random projections of smooth manifolds
- Volume estimate of submanifolds in compact Riemannian manifolds
- Volumes of compact manifolds
- Inferring solutions of differential equations using noisy multi-fidelity data
- Machine learning of linear differential equations using Gaussian processes
- Hidden physics models: machine learning of nonlinear partial differential equations
- The conditioning of Toeplitz band matrices
- IDENT: identifying differential equations with numerical time evolution
- Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem
- The Barron space and the flow-induced function spaces for neural network models
- Data-driven deep learning of partial differential equations in modal space
- Data-driven discovery of emergent behaviors in collective dynamics
- Machine learning for prediction with missing dynamics
- SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations
- Numerical aspects for approximating governing equations using data
- Data driven governing equations approximation using deep neural networks
- Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
- PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- Convergence and stability in the numerical integration of ordinary differential equations
- Automated reverse engineering of nonlinear dynamical systems
- Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- Robust data-driven discovery of governing physical laws with error bars
- An Introduction to Numerical Analysis
- A mean field view of the landscape of two-layer neural networks
- Deep Network With Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
- Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions
- Discovery of Dynamics Using Linear Multistep Methods
- Deep Network Approximation for Smooth Functions
- Deep Network Approximation Characterized by Number of Neurons
- Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities
- Nonparametric inference of interaction laws in systems of agents from trajectory data
- Dynamic systems identification with Gaussian processes
- A special stability problem for linear multistep methods
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