I am a researcher, designer, and practitioner driven by the pursuit of fundamental truths—elegant, universal principles that reveal beauty within complexity. My perspective is shaped by a fusion of disciplines: a deep understanding of AI/ML, a well-honed spatial intuition, and the rigor of mathematical thought. These facets intertwine, constantly sparking a dynamic interplay of ideas.

JUST A TECHNOLOGIST | AI+ROBOTICS RESEARCHER | ARCHITECT OF SPACES AND SYSTEMS

PARTICLES LAB ｜ EXP-1

Laplace Operator, Convolution, and the Propagation of Heat

EXP-1 draws inspiration from the heat equilibrium equation and the Laplace operator. It showcases how heat propagation across a 2D surface can be efficiently batch-computed through a grid-based convolution operation, offering a practical approximation to continuous gradient solvers. This approach brings inherent advantages, including parallelism, computational efficiency, and adaptability for downstream tasks like identifying global maxima. Unlike continuous gradient-based solvers, which often scale at O(N²) or higher due to global dependencies, the computational complexity of this grid-based method typically scales at O(N).

References
Daniel F. Styer. The geometrical significance of the Laplacian. American Journal of Physics, 2015.
Yann LeCun. Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 1995.
Blewitt et al. Applicability of GPGPU Computing to Real-Time AI Solutions in Games. IEEE Transactions on Computational Intelligence and AI in Games, 2013.