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Found 9 papers, 6 papers with code
Efficient geometric Markov chain Monte Carlo for nonlinear Bayesian inversion enabled by derivative-informed neural operators
Furthermore, the training cost of DINO surrogates breaks even after collecting merely 10--25 effective posterior samples compared to geometric MCMC.
Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators
We propose a novel machine learning framework for solving optimization problems governed by large-scale partial differential equations (PDEs) with high-dimensional random parameters.
Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems
We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs.
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning
We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest.
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs.
Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs
We use the projection basis vectors in the active subspace as well as the principal output subspace to construct the weights for the first and last layers of the neural network, respectively.
Ill-Posedness and Optimization Geometry for Nonlinear Neural Network Training
We show that the nonlinear activation functions used in the network construction play a critical role in classifying stationary points of the loss landscape.
Low Rank Saddle Free Newton: A Scalable Method for Stochastic Nonconvex Optimization
In this work we motivate the extension of Newton methods to the SA regime, and argue for the use of the scalable low rank saddle free Newton (LRSFN) method, which avoids forming the Hessian in favor of making a low rank approximation.
Inexact Newton Methods for Stochastic Non-Convex Optimization with Applications to Neural Network Training
We survey sub-sampled inexact Newton methods and consider their application in non-convex settings.
Optimization and Control Numerical Analysis
