Probabilistic partition of unity networks for high‐dimensional regression problems
DOI10.1002/nme.7207arXiv2210.02694OpenAlexW4318317725MaRDI QIDQ6062830
Unnamed Author, Eric Darve, Nathaniel Trask, Marta D'Elia
Publication date: 2 December 2023
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.02694
Nonparametric regression and quantile regression (62G08) Factor analysis and principal components; correspondence analysis (62H25) Probabilistic models, generic numerical methods in probability and statistics (65C20) Nonlinear parabolic equations (35K55) Quantum computation (81P68) Approximation by polynomials (41A10)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Lebesgue functions and Lebesgue constants in polynomial interpolation
- Learning constitutive relations from indirect observations using deep neural networks
- Kernel PCA for novelty detection
- Projection-based approximation and a duality with kernel methods
- Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
- Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
- DGM: a deep learning algorithm for solving partial differential equations
- Physics constrained learning for data-driven inverse modeling from sparse observations
- Learning generative neural networks with physics knowledge
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- Error bounds for approximations with deep ReLU networks
- Gradient-based optimization for regression in the functional tensor-train format
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Exploiting active subspaces to quantify uncertainty in the numerical simulation of the hyshot II scramjet
- Data-driven computational mechanics
- Non-intrusive low-rank separated approximation of high-dimensional stochastic models
- A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems
- Spectral Tensor-Train Decomposition
- Active Subspaces
- Reducing the Dimensionality of Data with Neural Networks
- Splines in Statistics
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Radial Basis Functions
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
- Solving high-dimensional partial differential equations using deep learning
- Solving parametric PDE problems with artificial neural networks
- EXTENDING CLASSICAL SURROGATE MODELING TO HIGH DIMENSIONS THROUGH SUPERVISED DIMENSIONALITY REDUCTION: A DATA-DRIVEN APPROACH
- Deep ReLU networks and high-order finite element methods
- Breaking the Curse of Dimensionality with Convex Neural Networks
This page was built for publication: Probabilistic partition of unity networks for high‐dimensional regression problems
