/Experiments

Computational experiments for my research

Primary LanguagePythonMIT LicenseMIT

Transformers

  • Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. Advances in neural information processing systems, 30.

Fourier Neural Operator

  • Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2021). Neural operator: Learning maps between function spaces. arXiv preprint arXiv:2108.08481.
  • Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895.

SINDy

  • de Silva, B. M., Champion, K., Quade, M., Loiseau, J. C., Kutz, J. N., & Brunton, S. L. (2020). Pysindy: a python package for the sparse identification of nonlinear dynamics from data. arXiv preprint arXiv:2004.08424.
  • 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.

MFcNN

  • Meng, X., & Karniadakis, G. E. (2020). A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. Journal of Computational Physics, 401, 109020.