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

TL;DR

PIVONet is a novel framework combining Neuro-ODEs and continuous normalizing flows to efficiently simulate stochastic fluid dynamics, capturing turbulence and randomness through a variational approach.

Contribution

It introduces a physically-informed variational Neuro-ODE model that efficiently simulates stochastic advection-diffusion fluids by integrating CNFs and variational inference.

Findings

Efficient surrogate fluid simulator trained offline.

Captures turbulence and stochasticity in fluid trajectories.

Uses variational ELBO for stochastic ODE integration.

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 {\theta}, 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 {\phi} 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).