Bullet VS NumPy

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.

In NumPy with @, dot() or matmul():

In NumPy with * or multiply(). ` or multiply()` can multiply 0D or more D arrays by element-wise multiplication.

Data science projects often use numpy. However, numpy objects are not JSON-serializable and therefore require conversion to standard python objects in order to be saved:

numpy: A library for scientific computing in Python

Python has become a preferred language for data analysis due to its simplicity and robust library ecosystem. Among these, NumPy stands out with its efficient handling of numerical data. Let’s say you’re working with numbers for large data sets—something Python’s native data structures may find challenging. That’s where NumPy arrays come into play, making numerical computations seamless and speedy.

I was looking at all the big projects like numpy, pytorch, flask, etc.

I wish the NumPy devs would more thoroughly consider adding full fluent API support, e.g. x.sqrt().ceil(). [Issue #24081]