SVISE documentation

The idea behind this package is that everything should flow through the SDELearner class. After defining an instance of this class, you can perform stochastic variational inference using any combination of prior and approximate posterior. Every SDELearner needs a SDE prior, a Diffusion prior, an approximate posterior over the state in the form of a Markov Gaussian process, a Likelihood, and a choice of quad rule from the list of 1D Quadrature rules.

Some useful extras for solving SDEs defined by an SDELearner, solving the Lyapunov equations, and computing gradients of a parametrized skew-symmetric matrix fast are provided in the Utilities.

Examples can be found in the experiments directory.

Package reference

• High-level interfaces
  • SDELearner
  • Sparse polynomial SDEs
  • Neural SDE
  • Sparse polynomial for SDEs with Newtonian drift
  • State estimation
• SDE prior
  • SDEPrior base class
  • Exact motion model
  • Sparse linear model
  • Second order sparse linear model
  • Sparse linear model of neighbours
• Diffusion prior
  • Diffusion prior base class
  • Diagonal diffusion prior base class
  • Constant diagonal diffusion prior
  • Sparse diagonal diffusion prior
• Markov Gaussian process
  • MarginalSDE base class
  • Spectral parametrization
  • Diagonal parametrization
• Likelihood
  • Likelihood base class
  • Diagonal Gaussian likelihood
• 1D Quadrature rules
  • Gauss legendre quadrature
  • Trapezoidal quadrature
  • QuadRule1D abstract base class
  • Gauss-Legendre quad rule
  • Unbiased Gauss-Legendre quad rule
• Utilities
  • Solve SDE
  • Euler Maruyama integration
  • Solve Lyapunov spectral
  • Solve Lyapunov diagonal
  • Skew symmetric matrix exp
• PCA
  • PCA

Indices and tables

• Index

• Module Index

• Search Page

Research references

• Course, K., Nair, P.B. State estimation of a physical system with unknown governing equations. Nature 622, 261–267 (2023). https://doi.org/10.1038/s41586-023-06574-8