SciMLWorkshop: Workshop Materials for Training in Scientific Computing and Scientific Machine Learning (SciML)
These exercises teach common workflows which involve SciML's tools like DifferentialEquations.jl, ModelingToolkit.jl DiffEqFlux.jl, and the connections to parts like stochastic differential equations and Bayesian estimation.
Difficulty Levels
The designation (B) is for "Beginner", meaning that a user new to the package should feel comfortable trying this exercise. An exercise designated (I) is for "Intermediate", meaning the user may want to have some previous background in DifferentialEquations.jl or try some (B) exercises first. The additional (E) designation is for "Experienced", which are portions of exercises which may take some work.
Overview
The exercises are described as follows:
- Exercise 1 is solving a simple stiff ordinary differential equation. This is an introductory exercise to get users acquainted with the syntax.
- Exercise 2 takes the user through solving a stiff ordinary differential equation and using the ModelingToolkit.jl to automatically convert the function to a symbolic form to derive the analytical Jacobian to speed up the solver. The same biological system is then solved with stochasticity, utilizing EnsembleProblems to understand 95% bounds on the solution. Finally, probabilistic programming is employed to perform Bayesian parameter estimation of the parameters against data.
- Exercise 3 takes the user through defining hybrid delay differential equation, that is a differential equation with events, and using differentiable programming techniques (automatic differentiation) to to perform gradient-based parameter estimation.
- Exercise 4 takes the user through differential-algebraic equation (DAE) modeling, the concept of index, and using both mass-matrix and implicit ODE representations. This will require doing a bit of math, but the student will understand how to change their equations to make their DAE numerically easier for the integrators.
- Exercise 5 has one build an acausal model, a DAE system through a component-based modeling approach. Using a tutorial model of an RC circuit (resistor and capacitor) plus some information about inductors, the user then builds new ModelingToolkit components for an inductor and generates an RLC circuit to be simulated.
- Exercise 6 takes the user through optimizing a PDE solver, utilizing automatic sparsity pattern recognition, automatic conversion of numerical codes to symbolic codes for analytical construction of the Jacobian, preconditioned GMRES, and setting up a solver for IMEX and GPUs, and compute adjoints of PDEs.
- Exercise 7 focuses on a chaotic orbit, utilizing parallel ensembles across supercomputers and GPUs to quickly describe phase space.
- Exercise 8 takes the user through training a neural stochastic differential equation, using GPU-acceleration and adjoints through Flux.jl's neural network framework to build efficient training codes.
- Exercise 9 is a deep dive into controls analysis on nonlinear models. The user starts by building an acausal model of a DC motor, which is augmented with a PI-controller that is tuned to control the actions of the motor.
This exercise worksheet is meant to be a living document leading new users through a deep dive of the SciML feature set. If you further suggestions or want to contribute new problems, please open an issue or PR at the SciMLWorkshop.jl repository.
Reproducibility
The documentation of this SciML package was built using these direct dependencies,
Status `~/_work/SciMLWorkshop.jl/SciMLWorkshop.jl/docs/Project.toml`
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`and using this machine and Julia version.
Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7513 32-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_CPU_THREADS = 4
JULIA_NUM_PRECOMPILE_TASKS = 4A more complete overview of all dependencies and their versions is also provided.
Status `~/_work/SciMLWorkshop.jl/SciMLWorkshop.jl/docs/Manifest.toml`
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[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.15.1+0
[0ac62f75] libass_jll v0.17.5+0
[1183f4f0] libdecor_jll v0.2.2+0
[8e53e030] libdrm_jll v2.4.134+0
[2db6ffa8] libevdev_jll v1.13.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[36db933b] libinput_jll v1.28.1+0
[b53b4c65] libpng_jll v1.6.59+1
[9a156e7d] libva_jll v2.23.0+0
[f27f6e37] libvorbis_jll v1.3.8+0
[009596ad] mtdev_jll v1.1.7+0
[1317d2d5] oneTBB_jll v2023.1.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[d8fb68d0] xkbcommon_jll v1.13.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`