sofa VS Bullet

I have explored various resources, including the official Sofa website, SofaPython3 website, and YouTube videos, yet I have not been successful in locating valuable guidance on initiating the learning process for Sofa using Python. I know how to write basic Python, but I find myself perplexed regarding the necessary steps to construct models and execute simulations effectively.

SOFA (Simulation Open Framework Architecture )

So far I found PyBullet, RobotPy, RobotDK, SOFA, and some others, but I wonder if there is something that is comparable or better than Unity 3D for this specific use case.

For typical game physics engines... not that much. Math libraries like Eigen or Blaze use lots of template metaprogramming techniques under the hood that can help when you're doing large batched matrix multiplications (since it can remove temporary allocations at compile-time and can also fuse operations efficiently, as well as applying various SIMD optimizations), but it doesn't really help when you need lots of small operations (with mat3 / mat4 / vec3 / quat / etc.). Typical game physics engines tend to use iterative algorithms for their solvers (Gauss-Seidel, PBD, etc...) instead of batched "matrix"-oriented ones, so you'll get less benefits out of Eigen / Blaze compared to what you typically see in deep learning / scientific computing workloads.

The codebases I've seen in many game physics engines seem to all roll their own math libraries for these stuff, or even just use SIMD (SSE / AVX) intrinsics directly. Examples: PhysX (https://github.com/NVIDIA-Omniverse/PhysX), Box2D (https://github.com/erincatto/box2d), Bullet (https://github.com/bulletphysics/bullet3)...

I suspect most C++ physics libraries like Box2D (https://github.com/erincatto/box2d) or Bullet3 (https://github.com/bulletphysics/bullet3) could really benefit a lot from SIMD.

No, they replaced Bullet with Jolt. That is considerably more than "some adjustment", regardless of what you think of the result.

Vulkan graphics via Intel GVK, and physics via Bullet

The first two have a bunch of great examples, and I’m tying them together by refactoring some of the THREE examples to fit the ECS paradigm defined in AFrame. then upping the ante by adding physics using AMMO, which is more challenging since it’s only a partial implementation of Bullet, and already poorly documented (yet popular) physics engine.

Plus, SM uses a system called bullet physics, I imagine this would be rather complex to rework into a modern engine such as Unreal or Unity (after all, the majority of performance issues come from the physics engine rather than the graphics engine)

The physics in HDT-SMP are actually being calculated outside of Skyrim's engine with Bullet, an open-source physics engine. So this isn't some limitation of Skyrim's engine.