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PyDimension

  • Welcome to PyDimension Documentation!

Tutorial 1. Scaling law discovery

  • Tutorial 1.1: Pattern search-based two level optimization
  • Tutorial 1.2: Gradient descent-based two level optimization
  • Tutorial 1.3: Cross material experiments
  • Tutorial 1.4: Cross scales experiments for pip flow
  • Tutorial 1.5: Cross validation experiments
  • Tutorial 1.6: Sensitivity analysis

Tutorial 2. ODEs/PDEs discovery

  • Tutorial 2.1: ODEs discovery in spring-mass-damper systems!

Resources

  • Related papers and contents
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Contents
  • Dimensional analysis + machine learning
  • Data-driven scientific discovery for PDEs
  • Articles
  • 中文资源

Related papers and contents

Contents

  • Dimensional analysis + machine learning
  • Data-driven scientific discovery for PDEs
  • Articles
  • 中文资源

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.

Articles#

  • AI4Science to empower the fifth paradigm of scientific discovery

中文资源#

  • 集智俱乐部-无量纲学习:机器学习识别无量纲数与标度律

  • 学习漫谈(28):量纲分析是锐利武器 - 戴世强

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Tutorial 2.1: ODEs discovery in spring-mass-damper systems!

By Xiaoyu Xie (Northwesern University, https://xiaoyuxie.top)
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