Video Notes | Scientific ML
Into to scientific machine learning (sciml) in Julia.
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.
- 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
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.