On the influence of over-parameterization in manifold based surrogates and deep neural operators
From MaRDI portal
Publication:2687573
DOI10.1016/j.jcp.2023.112008OpenAlexW4320718938MaRDI QIDQ2687573
Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em. Karniadakis
Publication date: 7 March 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.05071
over-parameterizationscientific machine learningneural operatorsBrusselator diffusion-reaction systemmanifold-based polynomial chaos expansion
Stochastic analysis (60Hxx) Artificial intelligence (68Txx) Probabilistic methods, stochastic differential equations (65Cxx)
Related Items
Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads, Reliable extrapolation of deep neural operators informed by physics or sparse observations, On the geometry transferability of the hybrid iterative numerical solver for differential equations, Learning stiff chemical kinetics using extended deep neural operators
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Adaptive sparse polynomial chaos expansion based on least angle regression
- Sparse pseudospectral approximation method
- Gaussian processes with built-in dimensionality reduction: applications to high-dimensional uncertainty propagation
- Uncertainty propagation using infinite mixture of gaussian processes and variational Bayesian inference
- Kernel PCA for novelty detection
- Sparse polynomial chaos expansions via compressed sensing and D-optimal design
- Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
- Compressive sensing adaptation for polynomial chaos expansions
- Bayesian neural networks for uncertainty quantification in data-driven materials modeling
- Least squares polynomial chaos expansion: a review of sampling strategies
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Sparse pseudo spectral projection methods with directional adaptation for uncertainty quantification
- Basis adaptive sample efficient polynomial chaos (BASE-PC)
- An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
- Adaptive multi-element polynomial chaos with discrete measure: algorithms and application to SPDEs
- A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
- A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems
- Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- Polynomial Chaos in Stochastic Finite Elements
- Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
- Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- EXTENDING CLASSICAL SURROGATE MODELING TO HIGH DIMENSIONS THROUGH SUPERVISED DIMENSIONALITY REDUCTION: A DATA-DRIVEN APPROACH
- Theoretical issues in deep networks
- Reconciling modern machine-learning practice and the classical bias–variance trade-off
- Adaptive Smolyak Pseudospectral Approximations