Physics Discovery: SINDy + Conservation Laws + Symbolic Regression

Three ways to pull physics back out of raw trajectory data. SINDy fits a sparse handful of terms from a candidate library and recovers the actual equations of motion for systems like the Van der Pol oscillator. A kernel method asks instead what stays constant along the motion, finding conserved quantities without being told their form. Symbolic regression evolves expression trees until one of them rediscovers a closed-form law, like the pendulum period. Same data, three different questions: what are the dynamics, what is invariant, and what is the law.