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Found 16 papers, 12 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.
Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport
We tackle this challenging Bayesian inference problem using a likelihood-free approach based on measure transport together with the construction of summary statistics for the image data.
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.
A stochastic Stein Variational Newton method
Meanwhile, Stein variational Newton (SVN), a Newton-like extension of SVGD, dramatically accelerates the convergence of SVGD by incorporating Hessian information into the dynamics, but also produces biased samples.
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.
An efficient method for goal-oriented linear Bayesian optimal experimental design: Application to optimal sensor placemen
Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data.
Optimization and Control Numerical Analysis Numerical Analysis
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.
Tensor train construction from tensor actions, with application to compression of large high order derivative tensors
We present a method for converting tensors into tensor train format based on actions of the tensor as a vector-valued multilinear function.
Numerical Analysis Numerical Analysis
Projected Stein Variational Gradient Descent
The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions.
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.
Projected Stein Variational Newton: A Fast and Scalable Bayesian Inference Method in High Dimensions
We propose a projected Stein variational Newton (pSVN) method for high-dimensional Bayesian inference.
Disentangled behavioural representations
Individual characteristics in human decision-making are often quantified by fitting a parametric cognitive model to subjects' behavior and then studying differences between them in the associated parameter space.
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
