让神经网络模拟耗散系统时保持能量衰减，避免不真实能量增长。
Metriplectic Conditional Flow Matching for Dissipative Dynamics
- 将保守与耗散部分分离建模，结合结构保持采样器。
- 长期推演中能量衰减更稳定，能量异常上升事件减少80%以上。
- 适合需要物理一致性模拟的机械系统建模任务。
Metriplectic条件流匹配（MCFM）在不违背基本物理原则的前提下学习耗散动力学。神经代理模型常引入能量并导致长期推演不稳定；MCFM则将保守-耗散分解嵌入向量场和结构保持采样器中。训练通过短时转移的条件流匹配实现，避免长程推演伴随的梯度计算。推理阶段采用Strang-prox算法，交替执行辛更新与近端度量步，确保离散能量衰减；当有可信能量函数时可选投影以强制严格衰减。本文提供了连续与离散时间保证，将该参数化与采样器与守恒性、单调耗散及稳定推演相联系。在受控机械基准测试中，MCFM生成的相图更接近真实轨迹，能量增加和正能量率事件显著少于同等表达力的无约束神经流，同时保持终端分布拟合效果。
原文摘要 · Abstract (English)
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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