From 5db9ea42e6849426d6c59c27c36ae62bd34d3185 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sun, 25 Aug 2024 18:09:22 +0000 Subject: [PATCH] build based on 12e6936 --- dev/.documenter-siteinfo.json | 2 +- dev/Contact.html | 2 +- dev/GSoC.html | 2 +- dev/api.html | 6 +++--- dev/examples.html | 2 +- dev/index.html | 2 +- dev/notes.html | 2 +- 7 files changed, 9 insertions(+), 9 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 8dc76ac..64d9d06 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-25T17:05:11","documenter_version":"1.6.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-25T18:09:19","documenter_version":"1.6.0"}} \ No newline at end of file diff --git a/dev/Contact.html b/dev/Contact.html index 130b6de..658588f 100644 --- a/dev/Contact.html +++ b/dev/Contact.html @@ -1,2 +1,2 @@ -Contact Developer · TrixiEnzyme.jl
GitHub

Contact Developer

If you have questions, suggestions, or are interested in contributing, feel free to reach out our developer, Junyi, via junyixu0@gmail.com.

+Contact Developer · TrixiEnzyme.jl
GitHub

Contact Developer

If you have questions, suggestions, or are interested in contributing, feel free to reach out our developer, Junyi, via junyixu0@gmail.com.

diff --git a/dev/GSoC.html b/dev/GSoC.html index 3f25fbe..80766ce 100644 --- a/dev/GSoC.html +++ b/dev/GSoC.html @@ -1,2 +1,2 @@ -GSoC · TrixiEnzyme.jl
GitHub

Final Report: GSoC '24

  • Student Name: Junyi(@junyixu).
  • Organization: Trixi Framework community.
  • Mentors: Michael(@sloede) and Hendrik(@ranocha)
  • Project: Integrating the Modern CFD Package Trixi.jl with Compiler-Based Auto-Diff via Enzyme.jl
  • Project Link: https://github.com/junyixu/TrixiEnzyme.jl

Project Overview

Trixi.jl is a numerical simulation framework for conservation laws written in Julia. The integration of Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl offers the following benefits: facilitates rapid forward mode AD, enables reverse mode AD, supports cross-language AD, and critically, supports mutating operations and caching, on which Trixi.jl relies, to enhance the performance of both simulation runs and AD. The final deliverable will include as many of Trixi's advanced features as possible, such as adaptive mesh refinement, shock capturing, etc., showcasing the benefits of differentiable programming in Julia's ecosystem.

  • Forward Mode Automatic Differentiation (AD) for Discontinuous Galerkin Collocation Spectral Element Method (DGSEM): Implement forward mode automatic differentiation to enhance the calculation of derivatives in DG methods, improving computational efficiency and accuracy for various applications.
  • Reverse Mode Automatic Differentiation for DG.
  • Improve Performance:
    • Extract Parameters Passed to Enzyme: Implement a systematic approach to extract and manage parameters passed to Enzyme, ensuring optimal configuration and efficiency in the execution of AD tasks.
    • batchsize for Jacobians:
      • Optimize for Memory Bandwidth: Fine-tune the batch size in Jacobian computations to optimize the use of memory bandwidth, thus improving the overall performance and speed of the computations.
      • Automatically Pick batchsize
  • Explore Enzyme Custom Rules: Investigate and implement custom rules within the Enzyme AD framework to handle specific cases and operations that are not optimally managed by the default settings, enhancing the flexibility and capability of the AD processes.

Please note that the last step was planned but remains incomplete due to time constraints and this step will be completed in the future if possible.

Constraints and Future Work

  • Make Reverse Mode AD Work with Polyester.jl: Address compatibility issues and integrate reverse mode AD with Polyester.jl for multithreading capabilities, aiming to enhance performance and scalability of the AD operations across different computing environments.
  • Integrate Enzyme with GPU Kernels: Extend the functionality of Enzyme by integrating it with GPU kernels, allowing AD operations to leverage the parallel processing power of GPUs.

Acknowledgments

The entire project, along with this blog website, is developed and maintained by Junyi(@junyixu). The whole project is under the guidance of two outstanding professors, Michael(@sloede) and Hendrik(@ranocha), from Trixi Framework community.

The project also received support from other Julia contributors, including Benedict from Trixi Framework community.

+GSoC · TrixiEnzyme.jl
GitHub

Final Report: GSoC '24

  • Student Name: Junyi(@junyixu).
  • Organization: Trixi Framework community.
  • Mentors: Michael(@sloede) and Hendrik(@ranocha)
  • Project: Integrating the Modern CFD Package Trixi.jl with Compiler-Based Auto-Diff via Enzyme.jl
  • Project Link: https://github.com/junyixu/TrixiEnzyme.jl

Project Overview

Trixi.jl is a numerical simulation framework for conservation laws written in Julia. The integration of Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl offers the following benefits: facilitates rapid forward mode AD, enables reverse mode AD, supports cross-language AD, and critically, supports mutating operations and caching, on which Trixi.jl relies, to enhance the performance of both simulation runs and AD. The final deliverable will include as many of Trixi's advanced features as possible, such as adaptive mesh refinement, shock capturing, etc., showcasing the benefits of differentiable programming in Julia's ecosystem.

  • Forward Mode Automatic Differentiation (AD) for Discontinuous Galerkin Collocation Spectral Element Method (DGSEM): Implement forward mode automatic differentiation to enhance the calculation of derivatives in DG methods, improving computational efficiency and accuracy for various applications.
  • Reverse Mode Automatic Differentiation for DG.
  • Improve Performance:
    • Extract Parameters Passed to Enzyme: Implement a systematic approach to extract and manage parameters passed to Enzyme, ensuring optimal configuration and efficiency in the execution of AD tasks.
    • batchsize for Jacobians:
      • Optimize for Memory Bandwidth: Fine-tune the batch size in Jacobian computations to optimize the use of memory bandwidth, thus improving the overall performance and speed of the computations.
      • Automatically Pick batchsize
  • Explore Enzyme Custom Rules: Investigate and implement custom rules within the Enzyme AD framework to handle specific cases and operations that are not optimally managed by the default settings, enhancing the flexibility and capability of the AD processes.

Please note that the last step was planned but remains incomplete due to time constraints and this step will be completed in the future if possible.

Constraints and Future Work

  • Make Reverse Mode AD Work with Polyester.jl: Address compatibility issues and integrate reverse mode AD with Polyester.jl for multithreading capabilities, aiming to enhance performance and scalability of the AD operations across different computing environments.
  • Integrate Enzyme with GPU Kernels: Extend the functionality of Enzyme by integrating it with GPU kernels, allowing AD operations to leverage the parallel processing power of GPUs.

Acknowledgments

The entire project, along with this blog website, is developed and maintained by Junyi(@junyixu). The whole project is under the guidance of two outstanding professors, Michael(@sloede) and Hendrik(@ranocha), from Trixi Framework community.

The project also received support from other Julia contributors, including Benedict from Trixi Framework community.

diff --git a/dev/api.html b/dev/api.html index 886c10b..03055e0 100644 --- a/dev/api.html +++ b/dev/api.html @@ -1,5 +1,5 @@ -API reference · TrixiEnzyme.jl
GitHub

The TrixiEnzyme Module

TrixiEnzyme — Module
TrixiEnzyme

TrixiEnzyme.jl is a component package of the Trixi.jl ecosystem and integrates Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl for hyperbolic partial differential equations (PDEs). The integration of Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl offers the following benefits: facilitates rapid forward mode AD, enables reverse mode AD, supports cross-language AD, and critically, supports mutating operations and caching, on which Trixi.jl relies, to enhance the performance of both simulation runs and AD. The final deliverable will include as many of Trixi's advanced features as possible, such as adaptive mesh refinement, shock capturing, etc., showcasing the benefits of differentiable programming in Julia's ecosystem.

source

Module Index

Detailed API

TrixiEnzyme.enzyme_rhs! — Method
enzyme_rhs!(du_ode::AbstractVector, u_ode::AbstractVector, mesh, equations, initial_condition, boundary_conditions, source_terms, solver, boundaries, _node_coordinates, cell_ids, node_coordinates, inverse_jacobian, _neighbor_ids, neighbor_ids, orientation, surface_flux_values, u)

The best thing to do for a user would be to separate out the things that you need to track through, make them arguments to the function, and then simply Duplicate on those.

source
TrixiEnzyme.jacobian_enzyme_forward — Function
jacobian_enzyme_forward(semi::SemidiscretizationHyperbolic)

Uses the right-hand side operator of the semidiscretization semi and forward mode automatic differentiation to compute the Jacobian J of the semidiscretization semi at state u0_ode.

jacobian_enzyme_forward(f!::F, x::AbstractArray; N = pick_batchsize(x)) where F <: Function

Uses the function f! and forward mode automatic differentiation to compute the Jacobian J

Examples

julia> x = -1:0.5:1;
+API reference · TrixiEnzyme.jl
GitHub
The TrixiEnzyme Module
TrixiEnzyme — Module
TrixiEnzyme
TrixiEnzyme.jl is a component package of the Trixi.jl ecosystem and integrates Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl for hyperbolic partial differential equations (PDEs). The integration of Trixi.jl with Compiler-Based (LLVM level) automatic differentiation via Enzyme.jl offers the following benefits: facilitates rapid forward mode AD, enables reverse mode AD, supports cross-language AD, and critically, supports mutating operations and caching, on which Trixi.jl relies, to enhance the performance of both simulation runs and AD. The final deliverable will include as many of Trixi's advanced features as possible, such as adaptive mesh refinement, shock capturing, etc., showcasing the benefits of differentiable programming in Julia's ecosystem.
source
Module Index
Detailed API
TrixiEnzyme.enzyme_rhs! — Method
enzyme_rhs!(du_ode::AbstractVector, u_ode::AbstractVector, mesh, equations, initial_condition, boundary_conditions, source_terms, solver, boundaries, _node_coordinates, cell_ids, node_coordinates, inverse_jacobian, _neighbor_ids, neighbor_ids, orientation, surface_flux_values, u)
The best thing to do for a user would be to separate out the things that you need to track through, make them arguments to the function, and then simply Duplicate on those.
source
TrixiEnzyme.jacobian_enzyme_forward — Function
jacobian_enzyme_forward(semi::SemidiscretizationHyperbolic)
Uses the right-hand side operator of the semidiscretization semi and forward mode automatic differentiation to compute the Jacobian J of the semidiscretization semi at state u0_ode.
jacobian_enzyme_forward(f!::F, x::AbstractArray; N = pick_batchsize(x)) where F <: Function
Uses the function f! and forward mode automatic differentiation to compute the Jacobian J
Examples
julia> x = -1:0.5:1;
 julia> batch_size = 2;
 julia> jacobian_enzyme_forward(TrixiEnzyme.upwind!, x, N=batch_size)
 5×5 Matrix{Float64}:
@@ -7,9 +7,9 @@
   0.2  -0.2  -0.0  -0.0  -0.0
  -0.0   0.2  -0.2  -0.0  -0.0
  -0.0  -0.0   0.2  -0.2  -0.0
- -0.0  -0.0  -0.0   0.2  -0.2
source
TrixiEnzyme.jacobian_enzyme_forward_closure — Method
jacobian_enzyme_forward_closure(semi::SemidiscretizationHyperbolic; N = pick_batchsize(semi))
Same as jacobian_enzyme_forward but with closure
Notes
I resolved issues related to type instability caused by closures, which is a known limitation of Enzyme.
I utilized closures here because they simplify the reuse of memory buffers and temporary variables without the need for explicit storage. let blocks create a new hard scope and optionally introduce new local bindings.
source
TrixiEnzyme.jacobian_enzyme_reverse_closure — Method
jacobian_enzyme_reverse_closure(semi::SemidiscretizationHyperbolic)
Same as jacobian_enzyme_reverse but with closure
Warning
Enzyme.jl does not play well with Polyester.jl and there are no plans to fix this soon.
source
TrixiEnzyme.jacobian_enzyme_forward_closure — Method
jacobian_enzyme_forward_closure(semi::SemidiscretizationHyperbolic; N = pick_batchsize(semi))
Same as jacobian_enzyme_forward but with closure
Notes
I resolved issues related to type instability caused by closures, which is a known limitation of Enzyme.
I utilized closures here because they simplify the reuse of memory buffers and temporary variables without the need for explicit storage. let blocks create a new hard scope and optionally introduce new local bindings.
source
TrixiEnzyme.jacobian_enzyme_reverse_closure — Method
jacobian_enzyme_reverse_closure(semi::SemidiscretizationHyperbolic)
Same as jacobian_enzyme_reverse but with closure
Warning
Enzyme.jl does not play well with Polyester.jl and there are no plans to fix this soon.
source
TrixiEnzyme.pick_batchsize — Function
pick_batchsize(x)
 pick_batchsize(semi)
Return a reasonable batch size for batched differentiation.
Arguments
  • x: AbstractArray
  • semi: SemidiscretizationHyperbolic in Trixi.jl
Notes
Inspired by https://github.com/EnzymeAD/Enzyme.jl/pull/1545/files
Warning
This function is experimental, and not part of the public API.
Examples
julia> pick_batchsize(rand(3))
 3
 
 julia> pick_batchsize(rand(20))
-11
source

+11
source
diff --git a/dev/examples.html b/dev/examples.html index 90ab352..a7ce60f 100644 --- a/dev/examples.html +++ b/dev/examples.html @@ -26,4 +26,4 @@ J2 = jacobian_enzyme_forward(semi;N=1) J3 = jacobian_enzyme_reverse(semi;N=1) -J1 == J2 +J1 == J2 diff --git a/dev/index.html b/dev/index.html index edb54ab..457fdd9 100644 --- a/dev/index.html +++ b/dev/index.html @@ -16,4 +16,4 @@ julia> @time jacobian_enzyme_forward(TrixiEnzyme.upwind!, x, N=11); 0.000332 seconds (307 allocations: 410.453 KiB)

If you do not explicitly provide a chunk size, TrixiEnzyme will try to guess one for you based on your input vector:

julia> x = -1:0.01:1;
 julia> @time jacobian_enzyme_forward(TrixiEnzyme.upwind!, x);
-  0.000327 seconds (307 allocations: 410.453 KiB)

Benchmark for a 401x401 Jacobian of TrixiEnzyme.upwind! (Lower is better): upwind benchmark Enyme(@batch) means applying Polyester.@batch to middlebatches.

+ 0.000327 seconds (307 allocations: 410.453 KiB)

Benchmark for a 401x401 Jacobian of TrixiEnzyme.upwind! (Lower is better): upwind benchmark Enyme(@batch) means applying Polyester.@batch to middlebatches.

diff --git a/dev/notes.html b/dev/notes.html index d41c609..7f952b9 100644 --- a/dev/notes.html +++ b/dev/notes.html @@ -1,3 +1,3 @@ Notes · TrixiEnzyme.jl
GitHub

Proof of reverse mode AD

Take the example of polar coordinate system $x = r \cos \theta, y = r \sin \theta$, according to the chain rule: compute_graph We use $t$ to represent the $n$-th layer in the tree. with the values of 1,2,3.

\[\frac{\partial y_1}{\partial x_1} = \frac{\partial y_1}{\partial v_4} \frac{\partial v_4}{\partial x_1} \implies \frac{\partial y_1}{\partial x_1} = \sum_{i(t)} \frac{\partial y_1}{\partial v_{t,i}} {\color{red}\frac{\partial v_{t,i}}{\partial x_1}}\]

\[\frac{\partial v_4}{\partial x_1} = \frac{\partial v_4}{\partial v_{-1}} \frac{\partial v_{-1}}{\partial x_1} + \frac{\partial v_4}{\partial v_1} \frac{\partial v_1}{\partial x_1} \implies {\color{red}\frac{\partial v_{t,i}}{\partial x_1}} = \sum_{j(t)} \frac{\partial v_{t,i}}{\partial v_{t-1, j}} \frac{\partial v_{t-1, j}}{\partial x_1}\]

\[\frac{\partial y_1}{\partial x_1} = \sum_{i(t)} \frac{\partial y_1}{\partial v_{t,i}} -\sum_{j(i)} \frac{\partial v_{t,i}}{\partial v_{t-1,j}} \frac{\partial v_{t-1,j}}{\partial x_1} = \sum_{j} \bar{v}_{t-1,j} \frac{\partial v_{t-1,j}}{\partial x_1}\]

where we define adjoint as

\[\bar{v}_{t-1, j} = \sum_i \bar{v}_{t, i} \frac{\partial v_{t,i}}{\partial v_{t-1,j}}.\]

For example (in this computing graph):

\[\bar{v}_0 = \bar{v}_{1,2} = \frac{\partial v_{2,1}}{\partial v_{1,2}} \bar{v}_{2,1} + \frac{\partial v_{2,2}}{\partial v_{1,2}} \bar{v}_{2,2}.\]

+\sum_{j(i)} \frac{\partial v_{t,i}}{\partial v_{t-1,j}} \frac{\partial v_{t-1,j}}{\partial x_1} = \sum_{j} \bar{v}_{t-1,j} \frac{\partial v_{t-1,j}}{\partial x_1}\]

where we define adjoint as

\[\bar{v}_{t-1, j} = \sum_i \bar{v}_{t, i} \frac{\partial v_{t,i}}{\partial v_{t-1,j}}.\]

For example (in this computing graph):

\[\bar{v}_0 = \bar{v}_{1,2} = \frac{\partial v_{2,1}}{\partial v_{1,2}} \bar{v}_{2,1} + \frac{\partial v_{2,2}}{\partial v_{1,2}} \bar{v}_{2,2}.\]