Contents

Video Notes | Scientific ML

Into to scientific machine learning (sciml) in Julia.

Youtube videos

What is scientific machine learning

Combine the best of two worlds of machine learning and regular modeling. Black-box algorithms and big data alone are not enough for complex scientific problems.

Machine learning

  • Let the algorithm find the structure (rule) in the data
  • Efficiency in high dimensional models
  • Faster to infer after the model is trained

Old school modeling (e.g. physical models)

  • Domain knowledge (laws, contraints)
  • Less requirement of data points
  • Quantification of uncertainties

Aim

Tackling complex real world problems.

  • Complex multiscale phenomena
  • High dimensional parameters
  • Sparse, intrusive, costly data
  • Small tolerance of failure (~1 ppb)
  • Uncertainty quantification

Application in physics problem

Rocket combustion simulation for engine design.

  • PDE models with billions of parameters (degrees of freedom)
  • Computationally expensive (e.g. compressible fluid dynamics): months for one case of 3D model
  • To get things faster: Reduced order models (ROMs)
    • Project the complex one (1B dof) to simpler one (1k dof)
    • Hourse instead of months
    • The ML part was trained by PDE simulation snapshots to compute low dim basis
    • Lift and learn apporach.