How much can one learn a partial differential equation from its solution?
From MaRDI portal
Publication:6645956
DOI10.1007/s10208-023-09620-zMaRDI QIDQ6645956
Yimin Zhong, Hong-Kai Zhao, Yuchen He
Publication date: 29 November 2024
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Inverse problems for PDEs (35R30) Initial value problems for linear higher-order PDEs (35G10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)
Cites Work
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- \(\mathcal H\)-matrix approximation for the operator exponential with applications
- Hidden physics models: machine learning of nonlinear partial differential equations
- IDENT: identifying differential equations with numerical time evolution
- Data-driven deep learning of partial differential equations in modal space
- Weak SINDy for partial differential equations
- Physics constrained learning for data-driven inverse modeling from sparse observations
- PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
- Efficient sum-of-exponentials approximations for the heat kernel and their applications
- Dynamical systems with multivalued integrals on a torus
- Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
- On the measure-preserving flow on the torus
- Eigenvalues of Positive Definite Kernels II
- THE ERGODIC PROPERTY OF THE CHARACTERISTICS ON A TORUS
- A Spectral Order Method for Inverting Sectorial Laplace Transforms
- Automated reverse engineering of nonlinear dynamical systems
- Eigenvalues of Positive Definite Kernels
- On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
- Learning partial differential equations via data discovery and sparse optimization
- Data-sparse approximation to the operator-valued functions of elliptic operator
- Subspace Pursuit for Compressive Sensing Signal Reconstruction
- Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation
- Asymptotic Theory of \(\boldsymbol \ell _1\) -Regularized PDE Identification from a Single Noisy Trajectory
- SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
- Sparse dynamics for partial differential equations
- Data-Driven Identification of Parametric Partial Differential Equations
- On Differential Equations on the Torus
- On the Eigenfunctions and Eigenvalues of the General Linear Elliptic Differential Operator
- On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators
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