Definition
GPU computing uses graphics processing units for general-purpose computation:
\text{GPU: thousands of cores} \rightarrow \text{massive data parallelism}
In SCU terms: GPU architecture naturally maps to α-field computation—each core evolves a local region of α.
Why GPUs for α-Field Physics
The α-field evolves locally at every point:
\partial_t \alpha(x) = f(\alpha(x), \nabla\alpha, \chi)
GPUs excel at this:
- Same operation at every grid point
- Local data access patterns
- High arithmetic intensity
GPU vs CPU Architecture
| Feature | CPU | GPU |
|---|---|---|
| Cores | ~16 | ~10,000 |
| Per-core speed | High | Lower |
| Memory bandwidth | 100 GB/s | 2 TB/s |
| Best for | Sequential | Parallel |
α-Field Applications
| Application | GPU Speedup | Why? |
|---|---|---|
| Molecular dynamics | 100× | N-body χ-mode forces |
| Deep learning | 50× | Matrix operations |
| Fluid simulation | 200× | Grid-based turbulence |
| Quantum chemistry | 30× | Resonant state calculations |
Programming Model
GPUs use SIMT (Single Instruction, Multiple Threads):
// Conceptual χ-mode evolution on GPU
for each grid point i (in parallel):
χ_new[i] = evolve(α[i], χ[i], neighbors[i])Thousands of χ-mode updates happen simultaneously.
Memory Hierarchy
GPU efficiency requires managing memory levels:
\text{Registers} \leftarrow \text{Shared} \leftarrow \text{Global} \leftarrow \text{Host}
Local α-values in fast memory; neighbors fetched efficiently.
Limitations
- Memory size: Limited to ~80GB (can't fit full cosmological α-field)
- Sequential code: Poor for non-parallel portions
- Precision: Sometimes limited to single precision
- Energy: High power consumption
The Key Insight
GPU parallelism mirrors α-field physics.
The α-field evolves everywhere simultaneously:
- GPU cores = local α-field computation
- Parallel execution = distributed dynamics
- Memory bandwidth = field communication
- Synchronization = global constraints
When a GPU computes fluid flow, it's modeling turbulent χ-mode dynamics the same way the universe computes them—in parallel, everywhere, at once.