How Inexact Models and Scientific Machine Learning Can Guide Decision Making in Quantitative Systems Pharmacology
December 15 2019 in Biology, Julia, Pharmacology, Science | Tags: differential equations, julia, pharmacology, pumas, qsp | Author: Christopher Rackauckas
Pre-clinical Quantitiative Systems Pharmacology (QSP) is about trying to understand how a drug target effects an outcome. If I effect this part of the biological pathways, how will it induce toxicity? Will it be effective?
Recently I have been pulling in a lot of technical collegues to help with the development of next generation QSP tooling. Without a background in biological modeling, I found it difficult to explain the "how" and "why" of pharmacological modeling. Why is it differential equations, and where do these "massively expensive global optimization" runs come from? What kinds of problems can you solve with such models when you know that they are only approximate?
To solve these questions, I took a step back and tried to explain a decision making scenario with a simple model, to showcase how playing with a model can allow one to distinguish … READ MORE
Neural Jump SDEs (Jump Diffusions) and Neural PDEs
June 5 2019 in Differential Equations, Julia, Mathematics, Stochastics | Tags: CUDA, differentiable programming, DifferentialEquations.jl, gpu, julia, stochastic differential equations | Author: Christopher Rackauckas
This is just an exploration of some new neural models I decided to jot down for safe keeping. DiffEqFlux.jl gives you the differentiable programming tools to allow you to use any DifferentialEquations.jl problem type (DEProblem) mixed with neural networks. We demonstrated this before, not just with neural ordinary differential equations, but also with things like neural stochastic differential equations and neural delay differential equations.
At the time we made DiffEqFlux, we were the “first to the gate” for many of these differential equations types and left it as an open question for people to find a use for these tools. And judging by the Arxiv papers that went out days after NeurIPS submissions were due, it looks like people now have justified some machine learning use cases for them. There were two separate papers … READ MORE
Video Blog: Developing and Editing Julia Packages
May 16 2017 in Julia, Programming | Tags: git, Gitkraken, julia, packages | Author: Christopher Rackauckas
Google Summer of Code is starting up, so I thought it would be a good time to share my workflow for developing my own Julia packages, as well as my workflow for contributing to other Julia packages. This does not assume familiarity with commandline Git, and instead shows you how to use a GUI (GitKraken) to make branches and PRs, as well as reviewing and merging code. You can think of it as an update to my old blog post on package development in Julia. However, this is not only updated but also improved since I am now able to walk through the “non-code” parts of package developing (such as setting up AppVeyor and code coverage).
Enjoy! (I quite like this video blog format: it was a lot less work)
6 Months of DifferentialEquations.jl: Where We Are and Where We Are Going
December 15 2016 in Differential Equations, Julia, Mathematics, Programming, Stochastics, Uncategorized | Tags: DifferentialEquations.jl, julia | Author: Christopher Rackauckas
So around 6 months ago, DifferentialEquations.jl was first registered. It was at first made to be a library which can solve “some” types of differential equations, and that “some” didn’t even include ordinary differential equations. The focus was mostly fast algorithms for stochastic differential equations and partial differential equations.
Needless to say, Julia makes you too productive. Ambitions grew. By the first release announcement, much had already changed. Not only were there ordinary differential equation solvers, there were many. But the key difference was a change in focus. Instead of just looking to give a production-quality library of fast methods, a major goal of DifferentialEquations.jl became to unify the various existing packages of Julia to give one user-friendly interface.
Since that release announcement, we have made enormous progress. At this point, I believe we have both the most expansive and flexible … READ MORE
Introducing DifferentialEquations.jl
August 1 2016 in Differential Equations, FEM, Julia, Programming, Stochastics | Tags: DifferentialEquations.jl, julia | Author: Christopher Rackauckas
Edit: This post is very old. See this post for more up-to-date information.
Differential equations are ubiquitous throughout mathematics and the sciences. In fact, I myself have studied various forms of differential equations stemming from fields including biology, chemistry, economics, and climatology. What was interesting is that, although many different people are using differential equations for many different things, pretty much everyone wants the same thing: to quickly solve differential equations in their various forms, and make some pretty plots to describe what happened.
The goal of DifferentialEquations.jl is to do exactly that: to make it easy solve differential equations with the latest and greatest algorithms, and put out a pretty plot. The core idea behind DifferentialEquations.jl is that, while it is easy to describe a differential equation, they have such diverse behavior that experts have spent over a century compiling … READ MORE
Using Julia’s Type System For Hidden Performance Gains
June 7 2016 in Julia, Programming | Tags: DifferentialEquations.jl, julia, performance | Author: Christopher Rackauckas
What I want to share today is how you can use Julia’s type system to hide performance gains in your code. What I mean is this: in many cases you may find out that the optimal way to do some calculation is not a “clean” solution. What do you do? What I want to do is show how you can define special arrays which are wrappers such that these special “speedups” are performed in the background, while having not having to keep all of that muck in your main algorithms. This is easiest to show by example.
The examples I will be building towards are useful for solving ODEs and SDEs. Indeed, these tricks have all been implemented as part of DifferentialEquations.jl and so these examples come from a real use case! They really highlight a main feature of Julia: … READ MORE
Finalizing Your Julia Package: Documentation, Testing, Coverage, and Publishing
May 16 2016 in Julia | Tags: AppVoyer, coverage, documentation, Documenter.jl, julia, testing, Travis.CI | Author: Christopher Rackauckas
In this tutorial we will go through the steps to finalizing a Julia package. At this point you have some functionality you wish to share with the world… what do you do? You want to have documentation, code testing each time you commit (on all the major OSs), a nice badge which shows how much of the code is tested, and put it into metadata so that people could install your package just by typing Pkg.add(“Pkgname”). How do you do all of this?
Note: At anytime feel free to checkout my package repository DifferentialEquations.jl which should be a working example.
Generate the Package and Get it on Github
First you will want to generate your package and get it on Github repository. Make sure you have a Github account, and then setup the environment variables in the git shell:
Optimal Number of Workers for Parallel Julia
April 16 2016 in HPC, Julia, Programming, Stochastics | Tags: BLAS, hyperthreading, julia, parallel computing, workers | Author: Christopher Rackauckas
How many workers do you choose when running a parallel job in Julia? The answer is easy right? The number of physical cores. We always default to that number. For my Core i7 4770K, that means it’s 4, not 8 since that would include the hyperthreads. On my FX8350, there are 8 cores, but only 4 floating-point units (FPUs) which do the math, so in mathematical projects, I should use 4, right? I want to demonstrate that it’s not that simple.
Where the Intuition Comes From
Most of the time when doing scientific computing you are doing parallel programming without even knowing it. This is because a lot of vectorized operations are “implicitly paralleled”, meaning that they are multi-threaded behind the scenes to make everything faster. In other languages like Python, MATLAB, and R, this is also the case. Fire up MATLAB … READ MORE
Benchmarks of Multidimensional Stack Implementations in Julia
March 20 2016 in Julia, Programming | Tags: benchmark, data structures, julia, stack | Author: Christopher Rackauckas
Datastructures.jl claims it’s fast. How does it do? I wrote some quick codes to check it out. What I wanted to do is find out which algorithm does best for implementing a stack where each element is three integers. I tried filling a pre-allocated array, pushing into three separate vectors, and different implementations of the stack from the DataStructures.jl package.
function baseline()
stack = Array{Int64,2}(1000000,3)
for i=1:1000000,j=1:3
stack[i,j]=i
end
end
function baseline2()
stack = Array{Int64,2}(1000000,3)
for j=1:3,i=1:1000000
stack[i,j]=i
... READ MORE
Interfacing with a Xeon Phi via Julia
March 4 2016 in C, HPC, Julia, Programming, Stochastics, Xeon Phi | Tags: C, julia, MIC, OpenMP, parallel, Xeon Phi | Author: Christopher Rackauckas
(Disclaimer: This is not a full-Julia solution for using the Phi, and instead is a tutorial on how to link OpenMP/C code for the Xeon Phi to Julia. There may be a future update where some of these functions are specified in Julia, and Intel’s compilertools.jl looks like a viable solution, but for now it’s not possible.)
Intel’s Xeon Phi has a lot of appeal. It’s an instant cluster in your computer, right? It turns out it’s not quite that easy. For one, the installation process itself is quite tricky, and the device has stringent requirements for motherboard choices. Also, making out at over a taraflop is good, but not quite as high as NVIDIA’s GPU acceleration cards.
However, there are a few big reasons why I think our interest in the Xeon Phi should be renewed. For one, Intel … READ MORE