nathanaelbosch / ProbNumDiffEq.jl

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
MIT License
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Add an API to specify non-zero observation noise #298

Closed nathanaelbosch closed 7 months ago

nathanaelbosch commented 7 months ago

In our solver formulation we have an observation model of the form $$z_i \sim \mathcal{N} \left( z_i; \dot{y}(t_i) - f(y(t_i), t_i), R \right),$$ which, together with the zero-data ${z_i = 0}$ define the information operator of the solver. Currently, we always assume $R=0$ as we are concerned with solving ODEs. But, the algorithm would in principle also work with $R>0$, which could be e.g. used when solving discretized PDEs [1]. So let's add this.

[1] "Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations", Krämer et al, AISTATS (2022)