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PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation

Published: January 6, 2026 | arXiv ID: 2601.03397v1

By: Hei Shing Cheung, Qicheng Long, Zhiyue Lin

Potential Business Impact:

Simulates messy fluid motion with less math.

Business Areas:
Simulation Software

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).

Country of Origin
🇨🇦 Canada

Page Count
14 pages

Category
Computer Science:
Computational Engineering, Finance, and Science