Getting Started with Julia's SciML for the Python User

If you're a Python user who has looked into Julia, you're probably wondering what is the equivalent to SciPy is. And you found it: it's the SciML ecosystem! To a Python developer, SciML is SciPy, but with the high-performance GPU, capabilities of PyTorch, and neural network capabilities, all baked right in. With SciML, there is no “separate world” of machine learning sublanguages: there is just one cohesive package ecosystem.

Why SciML? High-Level Workflow Reasons

• Performance - The key reason people are moving from SciPy 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.
• 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.
• Composable Library Components - In Python 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, SciPy in yellow represents Python's most commonly used solvers:

Need Help Translating from Python to Julia?

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

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

Python to Julia SciML Functionality Translations

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

Why is Differentiable Programming Important for Scientific Computing?

Check out this blog post that goes into detail on how training neural networks in tandem with simulation improves performance by orders of magnitude. But can't you use analytical adjoint definitions? You can, but there are tricks to mix automatic differentiation into the adjoint definitions for a few orders of magnitude improvement too, as explained in this blog post.

These facts, along with many others, compose to algorithmic improvements with the implementation improvements, which leads to orders of magnitude improvements!