From Physics to Probability: Hamiltonian Mechanics for Generative Modeling and MCMC

Hamiltonian mechanics is a way to describe how physical systems, like planets or pendulums, move over time, focusing on energy rather than just forces. By reframing complex dynamics through energy lenses, this 19th-century physics framework now powers cutting-edge generative AI. It uses generalized coordinates ( q ) (like position) and their conjugate momenta ( p ) (related to momentum), forming a phase space that captures the system's state. This approach is particularly useful for complex systems with many parts, making it easier to find patterns and conservation laws. The post From Physics to Probability: Hamiltonian Mechanics for Generative Modeling and MCMC appeared first on Towards Data Science.

Mar 28, 2025 - 22:09

From Physics to Probability: Hamiltonian Mechanics for Generative Modeling and MCMC

Phase space of a nonlinear pendulum. Photo by the author.

Hamiltonian mechanics is a way to describe how physical systems, like planets or pendulums, move over time, focusing on energy rather than just forces. By reframing complex dynamics through energy lenses, this 19th-century physics framework now powers cutting-edge generative AI. It uses generalized coordinates \( q \) (like position) and their conjugate momenta \( p \) (related to momentum), forming a phase space that captures the system’s state. This approach is particularly useful for complex systems with many parts, making it easier to find patterns and conservation laws.