Finding Paths of Least Action with Gradient Descent
a year ago
- #physics
- #Lagrangian mechanics
- #optimization
- The post introduces a view of physics as optimization, focusing on minimizing the action to find paths of least action.
- It contrasts standard approaches (analytical and numerical) with a novel method using gradient descent for action minimization.
- The Lagrangian method is highlighted as a universal framework across physics fields, capable of describing various physical systems.
- A practical implementation demonstrates minimizing action with gradient descent, applied to a free body in a gravitational field.
- The approach successfully converges to the expected parabolic path, matching results from traditional ODE integration methods.
- Future directions include exploring more complex systems and quantum mechanics, alongside historical and philosophical implications of the action principle.