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An acceleration strategy for randomize-then-optimize sampling via deep neural networks
通过深度神经网络随机化然后优化采样的加速策略
ディープニューラルネットワークを介したサンプリングのランダム化と最適化のための加速戦略
심층 신경망을 통한 무작위 샘플링을 위한 가속화 전략
UNA ESTRATEGIA DE ACELERACIÓN PARA EL MUESTREO ALEATORIZADO Y LUEGO OPTIMIZADO A TRAVÉS DE REDES NEURALES PROFUNDAS
UNE STRATÉGIE D'ACCÉLÉRATION POUR L'ÉCHANTILLONNAGE ALÉATOIRE PUIS OPTIMISÉ VIA DES RÉSEAUX DE NEURAUX PROFONDS
Стратегия ускорения для рандомизации-затем-оптимизация выборки через глубокие нейронные сети
Liang Yan 闫亮 ¹, Tao Zhou 周涛 ²
¹ School of Mathematics, Southeast University, Nanjing Center for Applied Mathematics, Nanjing, 211135, China
中国 南京 东南大学数学学院南京应用数学中心
² LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
中国 北京 中国科学院 计算数学与科学工程计算研究所 科学与工程计算国家重点实验室
Journal of Computational Mathematics, 15 September 2021
Abstract

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO.

In particular, we propose to drawn the training points for the DNN-surrogate from a local approximated posterior distribution – yielding a flexible and efficient sampling algorithm that converges to the direct RTO approach. We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.
Journal of Computational Mathematics_1
Journal of Computational Mathematics_2
Journal of Computational Mathematics_3
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