diabayes.solver.ODESolver.bayesian_inversion#

ODESolver.bayesian_inversion(t: Float[Array, 'Nt'], mu: Float[Array, 'Nt'], noise_std: Float, y0: Variables, params: RSFParams | CNSParams, friction_constants: RSFConstants, block_constants: SpringBlockConstants | InertialSpringBlockConstants, Nparticles: int = 1000, Nsteps: int = 150, rng: None | int | Array = None) → BayesianSolution[source]#

A Bayesian inversion routine using the Stein Variational Inference method.

Parameters:

  • t (Array) – A vector or time values (in units of seconds). The time steps do not need to be uniform

  • mu (Array) – The observed friction curve sampled at t

  • noise_std (Float) – An estimate of the standard deviation of the noise in the measured friction curve. A conservative value is recommended, i.e. if the noise has a standard deviation of $10^{-3}$, a good starting point would be to set noise_std = 0.5e-3

  • y0 (Variables) – The initial values for the modelled friction and any state variables

  • params (_Params) – The initial guess for the invertible parameters that characterise the forward problem. It is recommended to use the result from ODESolver.max_likelihood_inversion. The prior distribution will be centered around this initial guess

  • friction_constants (_Constants) – The non-invertible constants that characterise the forward problem

  • block_constants (_BlockConstants) – The stress transfer constants (e.g. stiffness and loading rate)

  • Nparticles (int) – The number of particles (= posterior samples) to include. A higher value gives a more accurate estimation of the posterior distribution, at a higher computational cost.

  • Nsteps (int) – The number of iterations before convergence is expected to be achieved. It is recommended to start with a value of 100 and then see if an equilibrium was actually achieved. Increasing this value beyond the point of equilibrium does not do anything.

  • rng (None, int, jax.random.PRNGKey) – The random seed used to initialise the particle swarm distribution. If None, the current time will be used as a seed, which leads to different result for each realisation. When an integer is provided, a new jax.random.PRNGKey is generated.

Returns:

result – The result of the inversion incapsulated in a BayesianSolution container, which provides access to the full convergence chains, as well as diagnostic and visualisation routines.

Return type:

diabayes.BayesianSolution

Notes

This method is currently only compatible with standard rate-and-state friction models.