PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation
- URL: http://arxiv.org/abs/2601.03397v1
- Date: Tue, 06 Jan 2026 20:18:04 GMT
- Title: PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation
- Authors: Hei Shing Cheung, Qicheng Long, Zhiyue Lin,
- Abstract summary: We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integratesNeuro-ODEs with Continuous Normalizing Flows (CNFs) for fluid simulation and visualization.<n>First, we demonstrate that a physically informed model, parameterized by CNF parameters, can be trained offline to yield an efficient surrogate simulator for a specific fluid system.<n>Second, by introducing a variational model with parameters that captures latentity in observed fluid trajectories, we model the network output as a variational distribution and optimize a pathwise Lower Bound (ELBO)<n>
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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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