RDT Kernel

RDT Kernel is a physics-inspired numerical simulator implementing a nonlinear partial differential equation (PDE) for a scalar field L(x, y, t). It combines a logarithmic damping term with a Laplacian diffusion term, forming a compact PyTorch-based solver for recursive field dynamics, entropy stabilization, and nonlinear diffusion behavior.

This implementation uses PyTorch tensor operations, automatically runs on CPU or GPU (and TPU if available), and can function as a standalone simulator or a physics-based component within other systems.

Mathematical Model

The kernel evolves the field according to: ∂L/∂t = -α·ln(L) + D·∇²L

where:

• L(x, y, t): scalar field
• α: nonlinear damping coefficient
• D: diffusion constant
• ∇²L: discrete Laplacian

The equation models a nonlinear parabolic PDE coupling the field’s magnitude to its potential energy, creating self-stabilizing diffusion and entropy-bounded evolution.

Core Functions

• get_device(): Detects CPU, GPU, or TPU
• rdt_kernel(): Computes ∂L/∂t
• step(): Advances one Euler step with clamping
• run_demo(): Runs a full test simulation with timing and mean-field output

Installation

From PyPI: pip install rdt-kernel

From source: git clone https://github.com/RRG314/rdt-kernel.git cd rdt-kernel pip install .

Example

from rdt_kernel import run_demo run_demo(n=128, steps=100, alpha=0.5, D=0.1, dx=1.0, dt=0.01)

Example output: Running 100 steps on GPU... Done in 0.029s, mean=1.003536

Applications

• Nonlinear entropy and diffusion modeling
• Energy field evolution in dissipative media
• Recursive geometric and entropic systems
• Physics-inspired machine learning research

Author

Developed by Steven Reid (Independent Researcher) Repository: https://github.com/RRG314/rdt-kernel