Getting Started with Julia's SciML for the MATLAB User

If you're a MATLAB user who has looked into Julia for some performance improvements, you may have noticed that the standard library does not have all of the “batteries” included with a base MATLAB installation. Where's the ODE solver? Where's fmincon and fsolve? Those scientific computing functionalities are the pieces provided by the Julia SciML ecosystem!

Why SciML? High-Level Workflow Reasons

• Performance - The key reason people are moving from MATLAB to Julia's SciML in droves is performance. Even simple ODE solvers are much faster!, demonstrating orders of magnitude performance improvements for differential equations, nonlinear solving, optimization, and more. And the performance advantages continue to grow as more complex algorithms are required.
• Julia is quick to learn from MATLAB - Most ODE codes can be translated in a few minutes. If you need help, check out the QuantEcon MATLAB-Python-Julia Cheat Sheet.
• Package Management and Versioning - Julia's package manager takes care of dependency management, testing, and continuous delivery in order to make the installation and maintenance process smoother. For package users, this means it's easier to get packages with complex functionality in your hands.
• Free and Open Source - If you want to know how things are being computed, just look at our GitHub organization. Lots of individuals use Julia's SciML to research how the algorithms actually work because of how accessible and tweakable the ecosystem is!
• Composable Library Components - In MATLAB environments, every package feels like a silo. Functions made for one file exchange library cannot easily compose with another. SciML's generic coding with JIT compilation these connections create new optimized code on the fly and allow for a more expansive feature set than can ever be documented. Take new high-precision number types from a package and stick them into a nonlinear solver. Take a package for Intel GPU arrays and stick it into the differential equation solver to use specialized hardware acceleration.
• Easier High-Performance and Parallel Computing - With Julia's ecosystem, CUDA will automatically install of the required binaries and cu(A)*cu(B) is then all that's required to GPU-accelerate large-scale linear algebra. MPI is easy to install and use. Distributed computing through password-less SSH. Multithreading is automatic and baked into many libraries, with a specialized algorithm to ensure hierarchical usage does not oversubscribe threads. Basically, libraries give you a lot of parallelism for free, and doing the rest is a piece of cake.
• Mix Scientific Computing with Machine Learning - Want to automate the discovery of missing physical laws using neural networks embedded in differentiable simulations? Julia's SciML is the ecosystem with the tooling to integrate machine learning into the traditional high-performance scientific computing domains, from multiphysics simulations to partial differential equations.

In this plot, MATLAB in orange represents MATLAB's most commonly used solvers:

Need a case study?

Check out this talk from NASA Scientists getting a 15,000x acceleration by switching from Simulink to Julia's ModelingToolkit!

Need Help Translating from MATLAB to Julia?

The following resources can be particularly helpful when adopting Julia for SciML for the first time:

• QuantEcon MATLAB-Python-Julia Cheat Sheet
• The Julia Manual's Noteworthy Differences from MATLAB page
• Double-check your results with MATLABDiffEq.jl (automatically converts and runs ODE definitions with MATLAB's solvers)
• Use MATLAB.jl to more incrementally move code to Julia.

MATLAB to Julia SciML Functionality Translations

The following chart will help you get quickly acquainted with Julia's SciML Tools: