Title:
METHOD AND APPARATUS FOR BI-LEVEL PHYSICS-INFORMED NEURAL NETWORKS FOR PDE CONSTRAINED OPTIMIZATION
Document Type and Number:
WIPO Patent Application WO/2024/031525
Kind Code:
A1
Abstract:
A computer implemented method for solving Partial Differential Equation (PDE) constrained optimization problem with physics-informed neural networks (PINNs) is disclosed, wherein the optimization of state variables corresponding to solutions of PDE constraints and control variables corresponding to an optimization target are decoupled. The method comprises initializing weights of the PINNs and the control variables, wherein the solutions of PDE constraints are parameterized by the weights of the PINNs; calculating PDE losses related to the PDE constraints and an objective function related to the optimization target respectively; updating the control variables by a first learning rate with gradient descent of the objective function in one iteration under the condition of the weights of the PINNs are fixed; updating the weights of the PINNs by a second learning rate with gradient descent of the PDE losses in the same iteration under the condition of the updated control variables are fixed; and updating the control variables and the weights of the PINNs iteratively until convergence, wherein the updated weights of the PINNs in a last iteration are used for updating the control variables in a next iteration.
Inventors:
ZHU JUN (CN)
HAO ZHONGKAI (CN)
YING CHENGYANG (CN)
SU HANG (CN)
SONG JIAN (CN)
CHENG ZE (CN)
HAO ZHONGKAI (CN)
YING CHENGYANG (CN)
SU HANG (CN)
SONG JIAN (CN)
CHENG ZE (CN)
Application Number:
PCT/CN2022/111730
Publication Date:
February 15, 2024
Filing Date:
August 11, 2022
Export Citation:
Assignee:
BOSCH GMBH ROBERT (DE)
UNIV TSINGHUA (CN)
UNIV TSINGHUA (CN)
International Classes:
G06N3/04; G06F17/13; G06N3/08
Foreign References:
| CN114118405A | 2022-03-01 | |||
| CN114239698A | 2022-03-25 | |||
| CN114611678A | 2022-06-10 | |||
| US20210365616A1 | 2021-11-25 |
Other References:
PSAROS APOSTOLOS F, KAWAGUCHI KENJI, KARNIADAKIS GEORGE EM: "Meta-learning PINN loss functions", ARXIV.ORG, CORNELL UNIVERSITY LIBRARY, ARXIV.ORG, ITHACA, 12 July 2021 (2021-07-12), Ithaca, XP093137634, [retrieved on 20240305], DOI: 10.48550/arxiv.2107.05544
LORRAINE JONATHAN, VICOL PAUL, DUVENAUD DAVID: "Optimizing Millions of Hyperparameters by Implicit Differentiation", ARXIV (CORNELL UNIVERSITY), CORNELL UNIVERSITY LIBRARY, ARXIV.ORG, ITHACA, 6 November 2019 (2019-11-06), Ithaca, XP093137637, [retrieved on 20240305], DOI: 10.48550/arxiv.1911.02590
BROYDEN C. G.: "A class of methods for solving nonlinear simultaneous equations", MATHEMATICS OF COMPUTATION, AMERICAN MATHEMATICAL SOCIETY, US, vol. 19, no. 92, 1 January 1965 (1965-01-01), US , pages 577 - 593, XP093137646, ISSN: 0025-5718, DOI: 10.1090/S0025-5718-1965-0198670-6
RODOMANOV ANTON, NESTEROV YURII: "Greedy Quasi-Newton Methods with Explicit Superlinear Convergence", SIAM JOURNAL ON OPTIMIZATION, THE SOCIETY, PHILADELPHIA, PA,, US, vol. 31, no. 1, 1 January 2021 (2021-01-01), US , pages 785 - 811, XP093137649, ISSN: 1052-6234, DOI: 10.1137/20M1320651
LORRAINE JONATHAN, VICOL PAUL, DUVENAUD DAVID: "Optimizing Millions of Hyperparameters by Implicit Differentiation", ARXIV (CORNELL UNIVERSITY), CORNELL UNIVERSITY LIBRARY, ARXIV.ORG, ITHACA, 6 November 2019 (2019-11-06), Ithaca, XP093137637, [retrieved on 20240305], DOI: 10.48550/arxiv.1911.02590
BROYDEN C. G.: "A class of methods for solving nonlinear simultaneous equations", MATHEMATICS OF COMPUTATION, AMERICAN MATHEMATICAL SOCIETY, US, vol. 19, no. 92, 1 January 1965 (1965-01-01), US , pages 577 - 593, XP093137646, ISSN: 0025-5718, DOI: 10.1090/S0025-5718-1965-0198670-6
RODOMANOV ANTON, NESTEROV YURII: "Greedy Quasi-Newton Methods with Explicit Superlinear Convergence", SIAM JOURNAL ON OPTIMIZATION, THE SOCIETY, PHILADELPHIA, PA,, US, vol. 31, no. 1, 1 January 2021 (2021-01-01), US , pages 785 - 811, XP093137649, ISSN: 1052-6234, DOI: 10.1137/20M1320651
Attorney, Agent or Firm:
NTD PATENT & TRADEMARK AGENCY LTD. (CN)
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