JAX RB: Riemannian Brownian motion on manifolds

JAX RB is a library for Riemannian Brownian motion on constrained manifolds embedded in a vector space, or on quotient of such manifolds by a compact group. The theory is developed in [NgSo24]. Please refer to the github repository for installation instruction.

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Manifolds

• jax_rb.manifolds
  • Global Manifold
  • Sphere
  • Symmetric Positive Definite Matrix Manifold
  • Stiefel Manifold
  • Grassmann Manifold
  • Hypersurface with Diagonal constraints Manifold
  • Matrix Lie Group Left Invariant Metric
  • \(\mathrm{GL}^+(n)\) Generalized Linear Group Positive Determinant
  • \(\mathrm{Aff}^+(n)\) Affine Linear Group Positive Determinant
  • \(\mathrm{SL}(n)\) Special Linear Group
  • \(\mathrm{SO}(n)\) Special Orthogonal Group
  • \(\mathrm{SE}(n)\) Special Euclidean Group

Simulation

• jax_rb.simulation
  • Simulator
  • Matrix Lie Group Integrator
  • Global Manifold Integrator
  • Retractive Integrator

Utils

• jax_rb.utils
  • Utils

Indices and tables

• Index

• Module Index

• Search Page

Other Resources:

• Wikipedia
• GitHub
• Animation

References

[NgSo24]

Nguyen, D.; Sommer, S...: Second-order differential operators, stochastic differential equations and Brownian motions on embedded manifolds arXiv:2406.02879.