About this work

Research

This site documents ongoing experimental work on the Symplectic Residual Flow PINN — a physics-informed neural network architecture that preserves phase-space structure through a separable Hamiltonian formulation and Störmer-Verlet integration.

The central question is whether enforcing symplecticity in the hidden state can prevent gradient shattering as depth increases, making deep PINNs tractable for hard PDE benchmarks.

Architecture fixes

Two critical bugs were discovered and fixed during development. They are documented here because they affect the validity of any prior training runs.

Computation graph severed in LeapfrogLayer Fixed

Calling detach() inside the gradient helper broke the chain from physical coordinates to model output, so PDE derivatives were incorrect.

q_ = q.detach().requires_grad_(True)
p_ = p.detach().requires_grad_(True)

if not q.requires_grad:
    q = q.detach().requires_grad_(True)
if not p.requires_grad:
    p = p.detach().requires_grad_(True)

All prior SymplecticPINN PDE runs before this fix are invalid; the corrected model now responds to the PDE residual.

Non-separable Hamiltonian broke exact symplecticity Fixed

The original Hamiltonian network used one MLP over cat([q, p]), but explicit Stormer-Verlet is exactly symplectic only for separable Hamiltonians.

H = MLP(cat([q, p]))

H(q, p) = T(p) + V(q)
T_net: p -> scalar
V_net: q -> scalar

The corrected architecture supports the physical interpretation: kinetic energy plus potential energy in hidden phase space.

Contact

For questions about the research or this site, please get in touch.