基于神经场自动解码器的参数化稀薄流动的物理引导生成代理：流匹配与扩散的管道级研究
Physics-Guided Generative Surrogates for Parametric Rarefied Flows with Neural-Field Auto-Decoders: A Pipeline-Level Study of Flow Matching and Diffusion
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中文总结 AI 辅助
该研究提出一种物理引导的条件隐式生成框架，以神经场自动解码器为核心，通过流匹配与扩散技术实现参数化稀薄流动的高效代理建模，在稳态基准测试中表现出高精度，且具备向多值或随机解扩展的潜力。
中文摘要 AI 辅助
我们提出了一种用于参数化稀薄流动的条件隐式生成框架，该框架将神经场表示、隐式传输和冻结物理适配分离开来。神经场自动解码器将离散速度空腔解和直接模拟蒙特卡罗圆柱解压缩为共享坐标解码器。仅用于训练的主成分图支持条件流匹配（FM）和扩散，无需确定性的条件到隐式主干，而结构化低秩适配器会修正选定的解码器输出，同时上游管道保持冻结。在两个稳态基准测试中，冻结管道对样本外条件的插值精度为：空腔动力学相对L₁误差处于10⁻⁵量级，圆柱的每场面积加权均方根误差分别为密度0.038、温度0.041、速度低于0.01。对于空腔，物理适配使匹配网格的Bhatnagar–Gross–Krook诊断降低28.65%，同时保留场精度；对于圆柱，解析壁图严格施加无穿透条件，与学习到的FM适配器协同，使入口违反量降至0.277，全局质量平衡比降至冻结值的0.963，且场误差变化可忽略。与确定性的条件到图多层感知器进行的五种子控制对比显示，尽管在这些单值稳态问题上，生成管道的点精度未超过紧凑MLP，但结果验证了共享表示上基于采样的条件传输是一种有效的稳态代理，为多值或随机解族提供了自然途径。
英文摘要
We present a conditional latent generative framework for parametric rarefied flows that separates neural-field representation, latent transport, and frozen physics adaptation. Neural-field auto-decoders compress discrete-velocity cavity solutions and direct simulation Monte Carlo cylinder solutions into shared coordinate decoders. Train-only principal-component charts support conditional flow matching (FM) and diffusion without a deterministic condition-to-latent backbone, and structured low-rank adapters correct selected decoder outputs while the upstream pipeline remains frozen. On two steady benchmarks, the frozen pipelines interpolate out-of-sample conditions with cavity kinetic relative $L_1$ errors at the $10^{-5}$ level and cylinder per-field area-weighted RMSEs of 0.038 (density), 0.041 (temperature), and below 0.01 (velocities). For the cavity, physics adaptation reduces the matched-grid Bhatnagar--Gross--Krook diagnostic by 28.65% while preserving field accuracy; for the cylinder, the analytic wall map enforces no-penetration exactly and, jointly with the learned FM adapter, reduces the inlet violation to 0.277 and the global mass-balance ratio to 0.963 of the frozen values with negligible field-error change. A five-seed controlled comparison with deterministic condition-to-chart multilayer perceptrons shows that, although the generative pipelines do not surpass the compact MLP in point accuracy on these single-valued steady problems, the results validate sampling-based conditional transport on the shared representation as an effective steady surrogate, with a natural route to multivalued or stochastic solution families.
