Solving PDE-Constrained Control Problems Using Operator Learning

Authors: Rakhoon Hwang, Jae Yong Lee, Jin Young Shin, Hyung Ju Hwang4504-4512

AAAI 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We demonstrate the successful application of our method to various optimal control problems for different control variables with diverse PDE constraints from the Poisson equation to Burgers equation.In this section, we evaluate our method to handle a variety of PDE-constrained optimal control problems through four different examples.
Researcher Affiliation Academia Rakhoon Hwang* , 1 Jae Yong Lee* , 2 Jin Young Shin*, 3 Hyung Ju Hwang , 3 1POSTECH Institute of Artificial Intelligence 2Center for Artificial Intelligence and Natural Sciences, Korea Institute for Advanced Study 3Department of Mathematics, Pohang University of Science and Technology
Pseudocode No The paper describes its method verbally and with diagrams (Figure 1) but does not include any structured pseudocode or algorithm blocks.
Open Source Code No The paper does not contain any explicit statements about releasing source code for the methodology, nor does it provide any links to a code repository.
Open Datasets No The paper mentions using 'observed data' or generating data based on PDE formulations but does not provide concrete access information (link, DOI, specific repository, or formal citation with authors/year) for a publicly available or open dataset.
Dataset Splits No The paper mentions 'test data' and 'observed data' but does not provide specific dataset split information (exact percentages, sample counts, or citations to predefined splits) needed to reproduce the data partitioning.
Hardware Specification No The paper mentions 'computing power' in general but does not provide specific hardware details (exact GPU/CPU models, processor types, or memory amounts) used for running its experiments.
Software Dependencies Yes Alnæs, M.; Blechta, J.; Hake, J.; Johansson, A.; Kehlet, B.; Logg, A.; Richardson, C.; Ring, J.; Rognes, M. E.; and Wells, G. N. 2015. The FEni CS project version 1.5.
Experiment Setup Yes during our experiment, (x, y) Ω= [0, 1] [0, 1], α = 10 6, and ud = 1 2π2 sin πx sin πy.We set α = 0.01, Ω= [0, 1], T = 1, and t = 0.1. Also, we set the viscosity parameter ν = 0.01 to generate a shock wave.