Metriplectic Conditional Flow Matching for Dissipative Dynamics

• URL: http://arxiv.org/abs/2509.19526v1
• Date: Tue, 23 Sep 2025 19:46:54 GMT
• Title: Metriplectic Conditional Flow Matching for Dissipative Dynamics
• Abstract summary: conditional flow matching learns dissipative dynamics without violating first principles.<n>MCFM trains via conditional flow matching on short transitions, avoiding long rollout adjoints.<n>We provide continuous and discrete time guarantees linking this parameterization and sampler to conservation, monotonic dissipation, and stable rollouts.
• Score: 5.920407670799846
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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