symplectic-opt

Symplectic optimization and Hamiltonian dynamics for conservation-law-aware training.

Usage

use symplectic_opt::{SymplecticMatrix, SeparableHamiltonian};

// Symplectic matrices preserve the canonical form J
let m = SymplecticMatrix::identity(2);
assert!(m.is_symplectic());

// Separable Hamiltonian: H(q,p) = T(p) + V(q)
let h = SeparableHamiltonian::harmonic_oscillator(1);

// Störmer-Verlet integrator preserves energy
let (q, p) = h.stormer_verlet(&[1.0], &[0.0], 0.01, 1000);

Features

• Symplectic matrices: 2n×2n with M^T J M = J verification
• Hamiltonian systems: Separable H(q,p) = T(p) + V(q)
• Symplectic Euler (1st order) and Störmer-Verlet (2nd order) integrators
• Conservation law tracking: Energy and momentum monitoring
• Natural gradient descent: Fisher information matrix optimization on Riemannian manifolds

Tests

23 tests, all passing. cargo test to run.

License

MIT

Part of the SuperInstance OpenConstruct ecosystem.