Trixi.jl is a Julia package for adaptive high-order numerical simulations of conservation laws. It is designed to be simple to use for students and researchers, extensible for research and teaching, as well as efficient and suitable for high-performance computing.
Difficulty: Medium (up to hard, depending on the chosen subtasks)
Project size: 175 hours or 350 hours, depending on the chosen subtasks
Enzyme.jl is the Julia frontend of Enzyme, a modern automatic differentiation (AD) framework working at the level of LLVM code. It can provide fast forward and reverse mode AD and - unlike some other AD packages - supports mutating operations. Since Trixi.jl relies on mutating operations and caches for performance, this feature is crucial to obtain an implementation that works efficiently for both simulation runs and AD.
The overall goal of this project is to create a working prototype of Trixi.jl (or a subset thereof) using Enzyme.jl for AD, and to support as many of Trixi's advanced features as possible, such as adaptive mesh refinement, shock capturing etc.
Possible subtasks in this project include
Explore and implement forward/backward mode AD via Enzyme.jl for a simplified simulation for the 1D advection equation or the 1D compressible Euler equations (e.g., compute the Jacobian of the right-hand side evaluation Trixi.rhs! on a simple mesh in serial execution)
Explore and implement forward mode AD via Enzyme.jl of semidiscretizations provided by Trixi.jl, mimicking the functionality that is already available via ForwardDiff.jl
Explore and implement reverse mode AD via Enzyme.jl of semidiscretizations provided by Trixi.jl as required for modern machine learning tasks
Explore and implement AD via Enzyme.jl of full simulations combining semidiscretizations of Trixi.jl with time integration methods of OrdinaryDiffEq.jl
Related subtasks in this project not related directly to Enzyme.jl but using other packages include
Explore and implement means to improve the current handling of caches to simplify AD and differentiable programming with semidiscretizations of Trixi.jl in general, e.g., via PreallocationTools.jl.
Extend the current AD support based on ForwardDiff.jl to other functionality of Trixi.jl, e.g., shock capturing discretizations, MPI parallel simulations, and other features currently not supported
This project is good for both software engineers interested in the fields of numerical analysis and scientific machine learning as well as those students who are interested in pursuing graduate research in the field.
Recommended skills: Good knowledge of at least one numerical discretization scheme (e.g., finite volume, discontinuous Galerkin, finite differences); initial knowledge in automatic differentiation; preferably the ability (or eagerness to learn) to write fast code
Expected results: Contributions to state of the art and production-quality automatic differentiation tools for Trixi.jl
Mentors: Hendrik Ranocha, Michael Schlottke-Lakemper
Difficulty: Medium
Project size: 175 hours or 350 hours, depending on the chosen subtasks
Visualizing and documenting results is a crucial part of the scientific process. In Trixi.jl, we rely for visualization on a combination of pure Julia packages (such as Plots.jl and Makie.jl) and the open-source scientific visualization suite ParaView. While the Julia solutions are excellent for visualizing 1D and 2D data, ParaView is the first choice for creating publication-quality figures from 3D data.
Currently, visualization with ParaView is only possible after a simulation is finished and requires an additional postprocessing step, where the native output files of Trixi.jl are converted to VTK files using Trixi2Vtk.jl. This extra step makes it somewhat inconvenient to use, especially when the current state of a numerical solution is to be checked during a long, multi-hour simulation run.
The goal of this project is therefore to make such visualizations easier by introducing two significant improvements:
Add the capability to write out native VTKHDF files directly during a simulation, in serial and parallel.
Enable parallel in-situ visualization of the results, i.e., to visualize results by connecting ParaView to a currently running, parallel Trixi.jl simulation using the Catalyst API.
Both tasks are related in that they require the student to familiarize themselves with both the data formats internally used in Trixi.jl as well as the visualization pipelines of VTK/ParaView. However, they can be performed independently and thus this project is suitable for either a 175 hour or a 350 hour commitment, depending on whether one or both tasks are to be tackled.
This project is good for both software engineers interested in the fields of visualization and scientific data analysis as well as those students who are interested in pursuing graduate research in the field of numerical analysis and high-performance computing.
Recommended skills: Some knowledge of at least one numerical discretization scheme (e.g., finite volume, discontinuous Galerkin, finite differences) is helpful; initial knowledge about visualization or parallel processing; preferably the ability (or eagerness to learn) to write fast code.
Expected results: Scalable, production quality visualization of scientific results for Trixi.jl.
Mentors: Michael Schlottke-Lakemper, Benedict Geihe, Johannes Markert