BoundaryValueDiffEq.jl
DiffEqGPU.jl
| BoundaryValueDiffEq.jl | DiffEqGPU.jl | |
|---|---|---|
| 1 | 2 | |
| 40 | 267 | |
| - | 0.0% | |
| 9.3 | 8.1 | |
| 6 days ago | 6 days ago | |
| Julia | Julia | |
| GNU General Public License v3.0 or later | MIT License |
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BoundaryValueDiffEq.jl
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Old programming language is suddenly getting more popular again
This isn't theoretical too, here's an actual user who opened an issue where their MWE was using quaternions:
https://github.com/SciML/BoundaryValueDiffEq.jl/issues/52
This is how I found out it worked in the differential equation solver: users were using it. The issue was unrelated (they didn't define enough boundary conditions), so it's quite cool that it was useful to someone. It turns out the quaternions have use cases in 3D rotations:
https://en.wikipedia.org/wiki/Gimbal_lock
which is where this all comes in. Anyways, it's always cool to learn from users what your own library supports! That's really a Julia treat.
DiffEqGPU.jl
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2023 was the year that GPUs stood still
Indeed, and this year we created a system for compiling ODE code not just optimized CUDA kernels but also OneAPI kernels, AMD GPU kernels, and Metal. Peer reviewed version is here (https://www.sciencedirect.com/science/article/abs/pii/S00457...), open access is here (https://arxiv.org/abs/2304.06835), and the open source code is at https://github.com/SciML/DiffEqGPU.jl. The key that the paper describes is that in this case kernel generation is about 20x-100x faster than PyTorch and Jax (see the Jax compilation in multiple ways in this notebook https://colab.research.google.com/drive/1d7G-O5JX31lHbg7jTzz..., extra overhead though from calling Julia from Python but still shows a 10x).
The point really is that while deep learning libraries are amazing, at the end of the day they are DSL and really pull towards one specific way of computing and parallelization. It turns out that way of parallelizing is good for deep learning, but not for all things you may want to accelerate. Sometimes (i.e. cases that aren't dominated by large linear algebra) building problem-specific kernels is a major win, and it's over-extrapolating to see ML frameworks do well with GPUs and think that's the only thing that's required. There are many ways to parallelize a code, ML libraries hardcode a very specific way, and it's good for what they are used for but not every problem that can arise.
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Julia GPU-based ODE solver 20x-100x faster than those in Jax and PyTorch
Link to GitHub repo from the abstract: https://github.com/SciML/DiffEqGPU.jl
What are some alternatives?
DiffEqOperators.jl - Linear operators for discretizations of differential equations and scientific machine learning (SciML)
hn-search - Hacker News Search
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
jax - Composable transformations of Python+NumPy programs: differentiate, vectorize, JIT to GPU/TPU, and more
ModelingToolkit.jl - An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
DiffEqBase.jl - The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
NeuralPDE.jl - Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
SciMLSensitivity.jl - A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
DifferentialEquations.jl - Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
GPUODEBenchmarks - Comparsion of Julia's GPU Kernel based ODE solvers with other open-source GPU ODE solvers
fortran-lang.org - (deprecated) Fortran website