Documentation updates (#242)

nathanaelbosch · Jun 2, 2023 · d2a9bf9 · d2a9bf9
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diff --git a/docs/make.jl b/docs/make.jl
@@ -8,17 +8,17 @@ makedocs(
     pages=[
         "Home" => "index.md",
         "Tutorials" => [
-            "Getting Started" => "getting_started.md"
-            "Second Order ODEs and Energy Preservation" => "dynamical_odes.md"
-            "Differential Algebraic Equations" => "dae.md"
-            "Probabilistic Exponential Integrators" => "exponential_integrators.md"
-            "Parameter Inference" => "fenrir.md"
+            "Getting Started" => "tutorials/getting_started.md"
+            "Second Order ODEs and Energy Preservation" => "tutorials/dynamical_odes.md"
+            "Differential Algebraic Equations" => "tutorials/dae.md"
+            "Probabilistic Exponential Integrators" => "tutorials/exponential_integrators.md"
+            "Parameter Inference" => "tutorials/fenrir.md"
         ],
         "Solvers and Options" => [
             "solvers.md",
-            "diffusions.md",
-            "initialization.md",
             "priors.md",
+            "initialization.md",
+            "diffusions.md",
         ],
         "Benchmarks" => [
             "Multi-Language Wrapper Benchmark" => "benchmarks/multi-language-wrappers.md",

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -8,20 +8,13 @@ The implemented _ODE filters_ solve differential equations via Bayesian filterin
 
 For a short intro video, check out our [poster presentation at JuliaCon2021](https://www.youtube.com/watch?v=EMFl6ytP3iQ).
 
----
-
-__For more probabilistic numerics check out the [ProbNum](https://probnum.readthedocs.io/en/latest/) Python package.__
-It implements probabilistic ODE solvers, but also probabilistic linear solvers, Bayesian quadrature, and many filtering and smoothing implementations.
-
----
-
 ## Installation
 
 Run Julia, enter `]` to bring up Julia's package manager, and add the ProbNumDiffEq.jl package:
 
 ```
 julia> ]
-(v1.8) pkg> add ProbNumDiffEq
+(v1.9) pkg> add ProbNumDiffEq
 ```
 
 ## Getting Started
@@ -30,29 +23,57 @@ For a quick introduction check out the "[Solving ODEs with Probabilistic Numeric
 
 ## Features
 
-  - Two extended Kalman filtering-based probabilistic solvers: the explicit [`EK0`](@ref) and semi-implicit [`EK1`](@ref).
-  - Adaptive step-size selection (by default with PI control)
-  - On-line uncertainty calibration, for multiple different measurement models
-  - Dense output
-  - Sampling from the solution
-  - Callback support
-  - Convenient plotting through a Plots.jl recipe
-  - Automatic differentiation via ForwardDiff.jl
-  - Supports arbitrary precision numbers via BigFloats.jl
-  - Specialized solvers for second-order ODEs (demo will be added)
-  - Compatible with DAEs in mass-matrix ODE form (demo will be added)
+- Two extended Kalman filtering-based probabilistic solvers: the explicit [`EK0`](@ref) and semi-implicit [`EK1`](@ref).
+- Adaptive step-size selection with PI control;
+  fully compatible with [DifferentialEquations.jl's timestepping options](https://docs.sciml.ai/DiffEqDocs/stable/extras/timestepping/)
+- Online uncertainty calibration for multiple different diffusion models (see "[Diffusion models and calibration](@ref)")
+- [Dense output](@ref)
+- Sampling from the solution
+- Callback support
+- Convenient plotting through a [Plots.jl](https://docs.juliaplots.org/latest/) recipe
+- Automatic differentiation via [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl)
+- Arbitrary precision via Julia's built-in [arbitrary precision arithmetic](https://docs.julialang.org/en/v1/manual/integers-and-floating-point-numbers/#Arbitrary-Precision-Arithmetic)
+- Specialized solvers for second-order ODEs (see [Second Order ODEs and Energy Preservation](@ref))
+- Compatible with DAEs in mass-matrix ODE form (see [Solving DAEs with Probabilistic Numerics](@ref))
 
 
 ## [References](@id references)
 
-  - N. Bosch, P. Hennig, F. Tronarp: **Probabilistic Exponential Integrators** (2023)
-  - N. Bosch, F. Tronarp, P. Hennig: **Pick-and-Mix Information Operators for Probabilistic ODE Solvers** (2022)
-  - N. Krämer, N. Bosch, J. Schmidt, P. Hennig: **Probabilistic ODE Solutions in Millions of Dimensions** (2022)
-  - N. Bosch, P. Hennig, F. Tronarp: **Calibrated Adaptive Probabilistic ODE Solvers** (2021)
-  - F. Tronarp, S. Särkkä, and P. Hennig: **Bayesian ODE Solvers: The Maximum A Posteriori Estimate** (2021)
-  - N. Krämer, P. Hennig: **Stable Implementation of Probabilistic ODE Solvers** (2020)
-  - H. Kersting, T. J. Sullivan, and P. Hennig: **Convergence Rates of Gaussian Ode Filters** (2020)
-  - F. Tronarp, H. Kersting, S. Särkkä, and P. Hennig: **Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective** (2019)
-  - M. Schober, S. Särkkä, and P. Hennig: **A Probabilistic Model for the Numerical Solution of Initial Value Problems** (2018)
-
-More references on ODE filters and on probabilistic numerics in general can be found on the [probabilistic-numerics.org homepage](https://www.probabilistic-numerics.org/research/general/).
+The main references _for this package_ include:
+
+- N. Bosch, P. Hennig, F. Tronarp:
+  [**Probabilistic Exponential Integrators**](https://arxiv.org/abs/2305.14978)
+  (2023)
+- N. Bosch, F. Tronarp, P. Hennig:
+  [**Pick-and-Mix Information Operators for Probabilistic ODE Solvers**](https://proceedings.mlr.press/v151/bosch22a.html)
+  (2022)
+- N. Krämer, N. Bosch, J. Schmidt, P. Hennig:
+  [**Probabilistic ODE Solutions in Millions of Dimensions**](https://proceedings.mlr.press/v162/kramer22b.html)
+  (2022)
+- N. Bosch, P. Hennig, F. Tronarp:
+  [**Calibrated Adaptive Probabilistic ODE Solvers**](http://proceedings.mlr.press/v130/bosch21a.html)
+  (2021)
+- F. Tronarp, S. Särkkä, and P. Hennig:
+  [**Bayesian ODE Solvers: The Maximum A Posteriori Estimate**](https://link.springer.com/article/10.1007/s11222-021-09993-7)
+  (2021)
+- N. Krämer, P. Hennig:
+  [**Stable Implementation of Probabilistic ODE Solvers**](https://arxiv.org/abs/2012.10106v1)
+  (2020)
+- H. Kersting, T. J. Sullivan, and P. Hennig:
+  [**Convergence Rates of Gaussian Ode Filters**](https://link.springer.com/article/10.1007/s11222-020-09972-4)
+  (2020)
+- F. Tronarp, H. Kersting, S. Särkkä, and P. Hennig:
+  [**Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective**](https://link.springer.com/article/10.1007/s11222-019-09900-1)
+  (2019)
+- M. Schober, S. Särkkä, and P. Hennig:
+  [**A Probabilistic Model for the Numerical Solution of Initial Value Problems**](https://link.springer.com/article/10.1007/s11222-017-9798-7)
+  (2018)
+
+More references on ODE filters and on probabilistic numerics in general can be found on [probabilistic-numerics.org ](https://www.probabilistic-numerics.org/research/general/).
+
+
+## Related packages
+
+- [probdiffeq](https://pnkraemer.github.io/probdiffeq/): Fast and feature-rich filtering-based probabilistic ODE solvers in JAX.
+- [ProbNum](https://probnum.readthedocs.io/en/latest/): Probabilistic numerics in Python. It has not only probabilistic ODE solvers, but also probabilistic linear solvers, Bayesian quadrature, and many filtering and smoothing implementations.
+- [Fenrir.jl](https://github.com/nathanaelbosch/Fenrir.jl): Parameter-inference in ODEs with probabilistic ODE solvers. This package builds on ProbNumDiffEq.jl to provide a negative marginal log-likelihood function, which can then be used with an optimizer or with MCMC for parameter inference.
diff --git a/docs/src/initialization.md b/docs/src/initialization.md
@@ -48,8 +48,8 @@ Y^{(0)}(0) &= y_0, \\
 Y^{(1)}(0) &= f(y_0, 0).
 \end{aligned}
 ```
-And it turns out that we can also compute higher-order derivatives of ``y`` with the chain rule,
-which we can use to initialize ``Y^{(i)}(0)``.
+It turns out that we can also compute higher-order derivatives of ``y`` with the chain rule,
+and then use these to better initialize ``Y^{(i)}(0)``.
 This, done efficiently with Taylor-mode autodiff by using
 [TaylorIntegration.jl](https://perezhz.github.io/TaylorIntegration.jl/latest/),
 is what [`TaylorModeInit`](@ref) does.

diff --git a/docs/src/dae.md → docs/src/tutorials/dae.md b/docs/src/dae.md → docs/src/tutorials/dae.md
diff --git a/docs/src/dynamical_odes.md → docs/src/tutorials/dynamical_odes.md b/docs/src/dynamical_odes.md → docs/src/tutorials/dynamical_odes.md
diff --git a/docs/src/exponential_integrators.md → .../src/tutorials/exponential_integrators.md b/docs/src/exponential_integrators.md → .../src/tutorials/exponential_integrators.md
diff --git a/docs/src/fenrir.md → docs/src/tutorials/fenrir.md b/docs/src/fenrir.md → docs/src/tutorials/fenrir.md
diff --git a/docs/src/getting_started.md → docs/src/tutorials/getting_started.md b/docs/src/getting_started.md → docs/src/tutorials/getting_started.md