用神经微分方程+变分推理，高效模拟流体随机运动
PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation
- 结合物理约束与变分推断，构建流体随机演化模型
- 训练后可快速替代复杂流体仿真，支持湍流和随机波动
- 适合需要高效真实流体模拟的可视化与科学计算场景
我们提出PIVONet（物理信息变分神经常微分方程），一种将神经常微分方程（Neuro-ODEs）与连续归一化流（CNFs）融合的统一框架，用于随机流体模拟与可视化。首先，通过参数为θ的物理信息模型离线训练，获得特定流体系统的高效代理模拟器，无需显式求解完整动力学过程。其次，引入参数为ϕ的变分模型以捕捉观测流体轨迹中的潜在随机性，将网络输出建模为变分分布，并优化路径级证据下界（ELBO），实现能刻画湍流与随机波动的随机微分方程积分（对流-扩散行为）。该方法显著提升模拟效率并保留真实物理特性。
原文摘要 · Abstract (English)
We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and visualization. First, we demonstrate that a physically informed model, parameterized by CNF parameters θ, can be trained offline to yield an efficient surrogate simulator for a specific fluid system, eliminating the need to simulate the full dynamics explicitly. Second, by introducing a variational model with parameters ϕ that captures latent stochasticity in observed fluid trajectories, we model the network output as a variational distribution and optimize a pathwise Evidence Lower Bound (ELBO), enabling stochastic ODE integration that captures turbulence and random fluctuations in fluid motion (advection-diffusion behaviors).
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