Preface: machine-learning approaches for computational mechanics

doi:10.1007/s10483-023-2999-7

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (7): 1035-1038.doi: https://doi.org/10.1007/s10483-023-2999-7

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Preface: machine-learning approaches for computational mechanics

Z. LI¹, Guohui HU², Zhiliang WANG², G. E. KARNIADAKIS³

1. Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634, U.S.A.;
2. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China;
3. Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A.

Received:2023-06-16 Revised:2023-06-20 Online:2023-07-01 Published:2023-07-05

Abstract

Z. LI, Guohui HU, Zhiliang WANG, G. E. KARNIADAKIS. Preface: machine-learning approaches for computational mechanics. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1035-1038.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-023-2999-7

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[2] KIM, M. and LIN, G. Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns. Applied Mathematics and Mechanics(English Edition), 47(7), 1085-1100(2023)https://doi.org/10.1007/s10483-023-2991-9
[3] HE, Y. C., WANG, Z. C., XIANG, H., JIANG, X. M., and TANG, D. W. An artificial viscosity augmented physics-informed neural network for incompressible flow. Applied Mathematics and Mechanics (English Edition), 47(7), 1101-1110(2023)https://doi.org/10.1007/s10483-023-2993-9
[4] WU, W., DANEKER, M., JOLLEY, M. A., TURNER, K. T., and LU, L. Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics. Applied Mathematics and Mechanics (English Edition), 47(7), 1039-1068(2023)https://doi.org/10.1007/s10483-023-2995-8
[5] FUHG, J. N., KARMARKAR, A., KADEETHUM, T., YOON, H., and BOUKLAS, N. Deep convolutional Ritz method: parametric PDE surrogates without labeled data. Applied Mathematics and Mechanics (English Edition), 47(7), 1151-1174(2023)https://doi.org/10.1007/s10483-023-2992-6
[6] YOU, H. Q., XU, X., YU, Y., SILLING, S., D'ELIA, M., and FOSTER, J. Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures. Applied Mathematics and Mechanics (English Edition), 47(7), 1125-1150(2023)https://doi.org/10.1007/s10483-023-2996-8
[7] MAO, Z. P. and MENG, X. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions. Applied Mathematics and Mechanics (English Edition), 47(7), 1069-1084(2023)https://doi.org/10.1007/s10483-023-2994-7
[8] MENG, X. Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems. Applied Mathematics and Mechanics (English Edition), 47(7), 1111-1124(2023)https://doi.org/10.1007/s10483-023-2997-7
[9] WU, J., WANG, S. F., and PERDIKARIS, P. A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations. Applied Mathematics and Mechanics (English Edition), 47(7), 1199-1224(2023)https://doi.org/10.1007/s10483-023-2998-7

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