Metriplectic Conditional Flow Matching for Dissipative Dynamics
This addresses the problem of unstable long-horizon rollouts in neural surrogates for dissipative dynamics, which is incremental as it builds on existing flow matching methods.
The paper tackles the problem of learning dissipative dynamics without violating first principles, where neural surrogates often inject energy and destabilize long-horizon rollouts. The result is that MCFM yields phase portraits closer to ground truth and markedly fewer energy-increase and positive energy rate events than an unconstrained neural flow, while matching terminal distributional fit.
Metriplectic conditional flow matching (MCFM) learns dissipative dynamics without violating first principles. Neural surrogates often inject energy and destabilize long-horizon rollouts; MCFM instead builds the conservative-dissipative split into both the vector field and a structure preserving sampler. MCFM trains via conditional flow matching on short transitions, avoiding long rollout adjoints. In inference, a Strang-prox scheme alternates a symplectic update with a proximal metric step, ensuring discrete energy decay; an optional projection enforces strict decay when a trusted energy is available. We provide continuous and discrete time guarantees linking this parameterization and sampler to conservation, monotonic dissipation, and stable rollouts. On a controlled mechanical benchmark, MCFM yields phase portraits closer to ground truth and markedly fewer energy-increase and positive energy rate events than an equally expressive unconstrained neural flow, while matching terminal distributional fit.