Workshops by the Probabilistic Mechanics Laboratory
Welcome to the PML Workshop repository. We use this repository to disseminate the results of our research and make them accessible to the broader scientific community.
Content
The repository consists of the following Jupyter Notebooks:
1_simple_logistic_regression.ipynb:
- The simplest model: perceptron
- The basis of backpropagation: forward and backward passes
- Multilayer perceptron
2_PINN_sciann_Burgers.ipynb:
- Physics-informed neural networks
- Basic concepts and formulation
- Example using SciANN
3_hybrid_PINN.ipynb:
- Hybrid models combining physics-informed kernels and neural networks
- Cumulative damage example
Further reading
If you are interested in applied machine learning, physics-informed neural networks, and hybrid models, you might consider the following list of papers:
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F. A. C. Viana and A. K. Subramaniyan, "A survey of Bayesian calibration and physics-informed neural networks in scientific modeling," Archives of Computational Methods in Engineering, Vol. 28 (5), pp. 3801-3830, 2021. (DOI: 10.1007/s11831-021-09539-0).
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R. G. Nascimento and F. A. C. Viana, "Cumulative damage modeling with recurrent neural networks," AIAA Journal, Online First, 13 pages, 2020. (DOI: 10.2514/1.J059250).
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A. Dourado and F. A. C. Viana, "Physics-informed neural networks for missing physics estimation in cumulative damage models: a case study in corrosion fatigue," ASME Journal of Computing and Information Science in Engineering, Vol. 20 (6), 10 pages, 2020. (DOI: 10.1115/1.4047173).
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Y. A. Yucesan and F. A. C. Viana, "A physics-informed neural network for wind turbine main bearing fatigue," International Journal of Prognostics and Health Management, Vol. 11 (1), 2020. (ISSN: 2153-2648).