CAS4DL: Christoffel adaptive sampling for function approximation via deep learning
DOI10.1007/s43670-022-00040-8OpenAlexW4306411814MaRDI QIDQ2098302
Nick C. Dexter, Juan M. Cardenas, Ben Adcock
Publication date: 17 November 2022
Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2208.12190
Christoffel functionredundant dictionaryadaptive samplingdeep learningdeep neural networkssampling strategiessample efficiency
Monte Carlo methods (65C05) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15) Complexity and performance of numerical algorithms (65Y20) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Sampling theory in information and communication theory (94A20)
Uses Software
Cites Work
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- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Data driven approximation of parametrized PDEs by reduced basis and neural networks
- A set of orthogonal polynomials induced by a given orthogonal polynomial
- Large deformation shape uncertainty quantification in acoustic scattering
- Computation of induced orthogonal polynomial distributions
- Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression
- Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
- Numerical solution of the parametric diffusion equation by deep neural networks
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- Frames and numerical approximation. II: Generalized sampling
- Error bounds for approximations with deep ReLU networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Handbook of Uncertainty Quantification
- On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification
- Introduction to Uncertainty Quantification
- Spectral Methods for Uncertainty Quantification
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- Optimal weighted least-squares methods
- The Gap between Theory and Practice in Function Approximation with Deep Neural Networks
- Solving parametric PDE problems with artificial neural networks
- Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces
- Near-Optimal Sampling Strategies for Multivariate Function Approximation on General Domains
- Sparse Polynomial Approximation of High-Dimensional Functions
- Multivariate approximation of functions on irregular domains by weighted least-squares methods
- Deep ReLU networks and high-order finite element methods
- Frames and Numerical Approximation
- Adaptive Approximation by Optimal Weighted Least-Squares Methods
- Breaking the Curse of Dimensionality with Convex Neural Networks
- Optimal sampling rates for approximating analytic functions from pointwise samples
- An introduction to frames and Riesz bases
