A kernel framework for learning differential equations and their solution operators
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Publication:6496499
DOI10.1016/J.PHYSD.2024.134095MaRDI QIDQ6496499
Bamdad Hosseini, Da Long, Nicole Mrvaljević, Shandian Zhe
Publication date: 3 May 2024
Published in: Physica D (Search for Journal in Brave)
reproducing kernel Hilbert spacesoperator learningphysics informed machine learningequation discovery
Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Probabilistic methods, stochastic differential equations (65Cxx)
Cites Work
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- The Pricing of Options and Corporate Liabilities
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
- Machine learning of linear differential equations using Gaussian processes
- IDENT: identifying differential equations with numerical time evolution
- Model reduction and neural networks for parametric PDEs
- Gaussian process regression constrained by boundary value problems
- Learning dynamical systems from data: a simple cross-validation perspective. I: Parametric kernel flows
- The Barron space and the flow-induced function spaces for neural network models
- Augmented Gaussian random field: theory and computation
- Solving and learning nonlinear PDEs with Gaussian processes
- Numerical methods for mean field games based on Gaussian processes and Fourier features
- A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
- 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
- Learning dynamical systems from data: a simple cross-validation perspective. III: Irregularly-sampled time series
- Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
- Inverse problems: A Bayesian perspective
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- 10.1162/15324430260185646
- ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
- Automated reverse engineering of nonlinear dynamical systems
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Nonstationary inverse problems and state estimation
- Probabilistic Principal Component Analysis
- Kernel Mean Embedding of Distributions: A Review and Beyond
- Learning partial differential equations via data discovery and sparse optimization
- Stochastic finite element methods for partial differential equations with random input data
- Kernel Mode Decomposition and the Programming of Kernels
- Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
- Asymptotic Theory of \(\boldsymbol \ell _1\) -Regularized PDE Identification from a Single Noisy Trajectory
- Approximation of high-dimensional parametric PDEs
- Learning dynamical systems from data: a simple cross-validation perspective. IV: Case with partial observations
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