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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2601.03397 |
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| _version_ | 1866908750707687424 |
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| author | Cheung, Hei Shing Long, Qicheng Lin, Zhiyue |
| author_facet | Cheung, Hei Shing Long, Qicheng Lin, Zhiyue |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation Cheung, Hei Shing Long, Qicheng Lin, Zhiyue Computational Engineering, Finance, and Science Machine Learning 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). |
| title | PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation |
| topic | Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2601.03397 |