maruti-iitm/tripods_winter_school_2022

Practicum on Supervised Learning in Function Spaces

TRIPODS Winter School & Workshop on Interplay between Artificial Intelligence (AI) and Dynamical Systems

Practicum on Supervised Learning in Function Spaces

January 21st, 2022

Instructors:

• Paris Perdikaris (University of Pennsylvania, [email protected])
• Jacob Seidman (University of Pennsylvania, [email protected])
• Georgios Kissas (University of Pennsylvania, [email protected])

Schedule

Part 1 (11:00am-12:15pm EST)

Functional data and applications; Supervised learning in function spaces; Parametric vs non-parametric approaches; Applications highlights; Introduction to JAX.

Video, Slides, Code

Part 2 (12:30pm-1:30pm EST)

Deep operator networks (DeepONets): Formulation, theory, implementation aspects and applications.

Video, Slides, Code

Part 3 (2:30pm-3:30pm EST)

Fourier Neural Operators: Formulation, theory, implementation aspects and applications.

Video, Slides, Code

Part 4 (3:45pm-5:00pm EST)

Advanced topics: attention-based architectures; Applications to optimal control and climate modeling; Open challenges; Concluding remarks & discussion.

Video, Slides

Data-sets:

• Training data for the Darcy problem.
• Testing data for the Darcy problem.

To cite this repository:

@misc{perdikaris2022tripods,
  author = {Perdikaris, Paris and Seidman, Jacob and Kissas, Georgios},
  title = {Supervised Learning in Function Spaces},
  year = {2022},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/PredictiveIntelligenceLab/TRIPODS_Winter_School_2022}}
}

Caution: ⚠️The provided DeepONet and FNO implementations cannot be used for commercial purposes due to a patent by Brown University.⚠️