docs: add key highlights

docs/src/GSoC.md

@@ -4,7 +4,7 @@
 - Organization: Trixi Framework community.
 - Mentors: Michael([@sloede](https://github.com/sloede)) and Hendrik([@ranocha](https://github.com/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 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.
@@ -20,6 +20,29 @@ Trixi.jl is a numerical simulation framework for conservation laws written in Ju
 
 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.
 
+## Key Highlights
+
+### Function Prototyping
+
+- Functions intended for automatic differentiation with `Enzyme.autodiff` should adhere to specific naming conventions:
+    - Functions must start with `enzyme_`.
+		- The primary role of these functions is to unpack `semi.cache` and accurately recreate `cache` for effective use with Enzyme’s APIs.
+
+### Configuration
+
+- The functions `jacobian_enzyme_forward` and `jacobian_enzyme_reverse` are configured to behave similarly to `jacobian_ad_forward`, with the primary distinction being how `batchsize` is chosen:
+    - An alternative usage pattern involves defining new functions prefixed with `enzyme_` and passing them to `jacobian_enzyme_forward` or `jacobian_enzyme_reverse` for differentiation.
+
+### Optimization Strategies
+
+- To enhance performance, several optimization strategies are recommended:
+    - Reuse containers for shadow variables during middlebatching and utilize the `@batch` macro for multithreading acceleration to improve computational efficiency.
+    - Minimize the number of arguments extracted from `semi.cache` to reduce overhead and streamline computations.
+    - Current benchmarks for Enzyme indicate mixed results. In scenarios involving smaller caches, like in toy models, `jacobian_enzyme(semi)` performs better than `ForwardDiff`. However, in the context of Discontinuous Galerkin Collocation Spectral Element Method (DGSEM) simulations, the performance may lag behind `jacobian_ad_forward(semi)` due to the challenges associated with large cache sizes (`elements._surface_flux_values` and `cache.interfaces._u`) and the complexities involved in unpacking and recreating the cache.
+
+This package aims to provide a robust framework for integrating advanced differentiation techniques into Trixi, addressing both performance and usability to facilitate high-quality computational research and development.
+
+
 ## 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.