1. Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks
- Author
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Lye, Kjetil O., Mishra, Siddhartha, Ray, Deep, and Chandrashekar, Praveen
- Subjects
Optimization ,FOS: Computer and information sciences ,Computer Science - Machine Learning ,Computer science ,Active learning (machine learning) ,Computational Mechanics ,General Physics and Astronomy ,010103 numerical & computational mathematics ,CFD ,Deep learning ,Neural networks ,01 natural sciences ,Machine Learning (cs.LG) ,Surrogate model ,Feature (machine learning) ,FOS: Mathematics ,Shape optimization ,Mathematics - Numerical Analysis ,0101 mathematics ,Mathematics - Optimization and Control ,Artificial neural network ,Mechanical Engineering ,Constrained optimization ,Numerical Analysis (math.NA) ,Feedback loop ,Optimal control ,Computer Science Applications ,010101 applied mathematics ,Mechanics of Materials ,Optimization and Control (math.OC) ,Algorithm - Abstract
We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems. This algorithm is based on deep neural networks and its key feature is the iterative selection of training data through a feedback loop between deep neural networks and any underlying standard optimization algorithm. Numerical examples for optimal control, parameter identification and shape optimization problems for PDEs are provided to demonstrate that ISMO significantly outperforms a standard deep neural network based surrogate optimization algorithm as well as standard optimization algorithms., Computer Methods in Applied Mechanics and Engineering, 374, ISSN:0045-7825, ISSN:1879-2138
- Published
- 2020
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