Merge pull request #970 from SciML/docs___update___simulation_introdu…

…ction

Simulation introduction doc page update

docs/Project.toml

@@ -55,7 +55,7 @@ ModelingToolkit = "9.16.0"
 NonlinearSolve = "3.12"
 Optim = "1.9"
 Optimization = "3.25"
-OptimizationBBO = "0.2.1"
+OptimizationBBO = "0.3"
 OptimizationNLopt = "0.2.1"
 OptimizationOptimJL = "0.3.1"
 OptimizationOptimisers = "0.2.1"

docs/src/inverse_problems/optimization_ode_param_fitting.md

@@ -170,7 +170,7 @@ nothing # hide
 ```
 
 ---
-## [Citation](@id structural_identifiability_citation)
+## [Citation](@id optimization_parameter_fitting_citation)
 If you use this functionality in your research, please cite the following paper to support the authors of the Optimization.jl package:
 ```
 @software{vaibhav_kumar_dixit_2023_7738525,

docs/src/model_simulation/simulation_introduction.md

@@ -222,6 +222,17 @@ sol = solve(sprob, STrapezoid(); seed = 12345, abstol = 1e-1, reltol = 1e-1) # h
 plot(sol)
 ```
 
+### [SDE simulations with fixed time stepping](@id simulation_intro_SDEs_fixed_dt)
+StochasticDiffEq implements SDE solvers with adaptive time stepping. However, when using a non-adaptive solver (or using the `adaptive = false` argument to turn adaptive time stepping off for an adaptive solver) a fixed time step `dt` must be designated. Here we simulate the same `SDEProblem` which we struggled with previously, but using the non-adaptive [`EM`](https://en.wikipedia.org/wiki/Euler%E2%80%93Maruyama_method) solver and a fixed `dt`:
+```@example simulation_intro_sde
+sol = solve(sprob, EM(); dt = 0.001)
+sol = solve(sprob, EM(); dt = 0.001, seed = 1234567) # hide
+plot(sol)
+```
+We note that this approach also enables us to successfully simulate the SDE we previously struggled with.
+
+Generally, using a smaller fixed `dt` provides a more exact simulation, but also increases simulation runtime.
+
 ### [Scaling the noise in the chemical Langevin equation](@id simulation_intro_SDEs_noise_saling)
 When using the CLE to generate SDEs from a CRN, it can sometimes be desirable to scale the magnitude of the noise. This can be done by introducing a *noise scaling term*, with each noise term generated by the CLE being multiplied with this term. A noise scaling term can be set using the `@default_noise_scaling` option:
 ```@example simulation_intro_sde
@@ -336,4 +347,54 @@ circadian_model = @reaction_network begin
     d, P --> 0
 end
 ```
-This type of model will generate so called *variable rate jumps*. Simulation of such model is non-trivial (and Catalyst currently lacks a good interface for this). A detailed description of how to carry out jump simulations for models with time-dependant rates can be found [here](https://docs.sciml.ai/JumpProcesses/stable/tutorials/simple_poisson_process/#VariableRateJumps-for-processes-that-are-not-constant-between-jumps).
+This type of model will generate so called *variable rate jumps*. Simulation of such model is non-trivial (and Catalyst currently lacks a good interface for this). A detailed description of how to carry out jump simulations for models with time-dependant rates can be found [here](https://docs.sciml.ai/JumpProcesses/stable/tutorials/simple_poisson_process/#VariableRateJumps-for-processes-that-are-not-constant-between-jumps).
+
+
+---
+## [Citation](@id simulation_intro_citation)
+When you simulate Catalyst models in your research, please cite the corresponding paper(s) to support the simulation package authors. For ODE simulations:
+```
+@article{DifferentialEquations.jl-2017,
+ author = {Rackauckas, Christopher and Nie, Qing},
+ doi = {10.5334/jors.151},
+ journal = {The Journal of Open Research Software},
+ keywords = {Applied Mathematics},
+ note = {Exported from https://app.dimensions.ai on 2019/05/05},
+ number = {1},
+ pages = {},
+ title = {DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia},
+ url = {https://app.dimensions.ai/details/publication/pub.1085583166 and http://openresearchsoftware.metajnl.com/articles/10.5334/jors.151/galley/245/download/},
+ volume = {5},
+ year = {2017}
+}
+```
+For SDE simulations:
+```
+@article{rackauckas2017adaptive,
+  title={Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory},
+  author={Rackauckas, Christopher and Nie, Qing},
+  journal={Discrete and continuous dynamical systems. Series B},
+  volume={22},
+  number={7},
+  pages={2731},
+  year={2017},
+  publisher={NIH Public Access}
+}
+```
+For jump simulations:
+```
+@misc{2022JumpProcesses,
+  author       = {Isaacson, S. A. and Ilin, V. and Rackauckas, C. V.},
+  title        = {{JumpProcesses.jl}},
+  howpublished = {\url{https://github.com/SciML/JumpProcesses.jl/}},
+  year         = {2022}
+}
+@misc{zagatti_extending_2023,
+	title = {Extending {JumpProcess}.jl for fast point process simulation with time-varying intensities},
+	url = {http://arxiv.org/abs/2306.06992},
+	doi = {10.48550/arXiv.2306.06992},
+	publisher = {arXiv},
+	author = {Zagatti, Guilherme Augusto and Isaacson, Samuel A. and Rackauckas, Christopher and Ilin, Vasily and Ng, See-Kiong and Bressan, Stéphane},
+	year = {2023},
+}
+```