Modeling practice seems to be partitioned into scientific models defined by mechanistic differential equations and machine learning models defined by parameterizations of neural networks. While the ability for interpretable mechanistic models to extrapolate from little information is seemingly at odds with the big data “model-free” approach of neural networks, the next step in scientific progress is to utilize these methodologies together in order to emphasize their strengths while mitigating weaknesses. In this talk we will describe four separate ways that we are merging differential equations and deep learning through the power of the DifferentialEquations.jl and Flux.jl libraries. Data-driven hypothesis generation of model structure, automated real-time control of dynamical systems, accelerated of PDE solving, and memory-efficient deep learning workflows will all shown to be derived from this common computational structure … READ MORE

The ability to build robust array type abstractions without overhead is one of the most fantastic features of Julia. It can be surprising how much one can do with the idea of an array to end up with better code. In this blog post I want to show how you can utilize Julia’s interface tools and @generated functions to build these kinds of zero-cost abstractions.

What is a zero-cost abstraction?

First let’s define a zero-cost abstraction. A zero-abstraction is a coding tool that has a zero run time cost associated with using it. Essentially what it does is it transforms into the fastest possible code during compilation so that its use has no effect on the run time of your code.

Example: Diagonal Matrices

A quick example is simple type wrappers in Julia. An example of this from the standard library is the Diagonal … READ MORE