Related papers and contents
Contents
Related papers and contents#
If you are interested in learning about data-driven scientific discovery, there are some excellent papers and articles that you can use as a starting point. These resources, which can be found in top journals such as Science and Nature, will give you a strong foundation in data-driven scientific discovery and introduce you to the principles and techniques involved in using data to guide research and uncover new knowledge.
Dimensional analysis + machine learning#
Dimensionless learning: Xie, X., Samaei, A., Guo, J., Liu, W. K., & Gan, Z. (2022). Data-driven discovery of dimensionless numbers and governing laws from scarce measurements. Nature Communications, 13(1), 1-11.
Dimensional invariant Neural Network (DimensionNet): Saha, S., Gan, Z., Cheng, L., Gao, J., Kafka, O. L., Xie, X., … & Liu, W. K. (2021). Hierarchical deep learning neural network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering. Computer Methods in Applied Mechanics and Engineering, 373, 113452.
BuckiNet: Bakarji, J., Callaham, J., Brunton, S.L. et al. Dimensionally consistent learning with Buckingham Pi. Nature Computational Science, 2, 834–844 (2022).
Dimensionless machine learning: Villar, S., Yao, W., Hogg, D. W., Blum-Smith, B., & Dumitrascu, B. (2022). Dimensionless machine learning: Imposing exact units equivariance. arXiv preprint arXiv:2204.00887.
Dimensional homogeneity constrained gene expression programming (DHC-GEP): Ma, W., & Zhang, J. (2022). Dimensional homogeneity constrained gene expression programming for discovering governing equations from noisy and scarce data. arXiv preprint arXiv:2211.09679.
AI Feynman: Udrescu, S. M., & Tegmark, M. (2020). AI Feynman: A physics-inspired method for symbolic regression. Science Advances, 6(16), eaay2631.
Xu, Z., Zhang, X., Wang, S., & He, G. (2022). Artificial neural network based response surface for data-driven dimensional analysis. Journal of Computational Physics, 459, 111145.
Data-driven scientific discovery for PDEs#
Chen, Z., Liu, Y., & Sun, H. (2021). Physics-informed learning of governing equations from scarce data. Nature communications, 12(1), 1-13.
Lusch, B., Kutz, J. N., & Brunton, S. L. (2018). Deep learning for universal linear embeddings of nonlinear dynamics. Nature communications, 9(1), 1-10.
Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017). Data-driven discovery of partial differential equations. Science advances, 3(4), e1602614.
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the national academy of sciences, 113(15), 3932-3937.
Schmidt, M., & Lipson, H. (2009). Distilling free-form natural laws from experimental data. science, 324(5923), 81-85.
Floryan, D., & Graham, M. D. (2022). Data-driven discovery of intrinsic dynamics. Nature Machine Intelligence, 1-8.