Hamilton-Jacobi-Bellman Equation: Reinforcement Learning and Diffusion Models

Machine learning feels recent, but one of its core mathematical ideas dates back to 1952, when Richard Bellman published a seminal paper titled “On the Theory of Dynamic Programming” [6, 7], laying the foundation for optimal control and what we now call reinforcement learning. Later in the 50s, Bellman extended his work to continuous-time systems, turning the optimal condition into a PDE. What he later found was that this was identical to a result in physics published a century before (1840s), known as the Hamilton-Jacobi equation. ...

March 28, 2026 · 17 min · Daniel López Montero

Fusion Energy Simulation: Tokamak

I think there are 3 major milestones remaining for humanity, and one of them is clean and abundant energy. Fusion energy has the potential to provide a nearly limitless source of clean energy by replicating the processes that power the sun. However, achieving controlled fusion reactions on Earth has proven to be a formidable and very challenging task. The most well-known fusion prototype is the tokamak, which uses a magnetic field to confine the plasma within a toroidal chamber (doughnut-shaped). ...

December 20, 2025 · 19 min · Daniel López Montero