Open Access

ARTICLE

Uncertainty-Aware Physical Simulation of Neural Radiance Fields for Fluids

Haojie Lian¹, Jiaqi Wang¹, Leilei Chen^2,*, Shengze Li³, Ruochen Cao⁴, Qingyuan Hu⁵, Peiyun Zhao¹

1 Key Laboratory of In-Situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China
2 Henan International Joint Laboratory of Structural Mechanics and Computational Simulation, College of Architectural and Civil Engineering, Huanghuai University, Zhumadian, 463000, China
3 National Innovation Institute of Defense Technology, Academy of Military Science, Beijing, 100091, China
4 School of Software, Taiyuan University of Technology, Jinzhong, 030600, China
5 School of Science, Jiangnan University, Wuxi, 214122, China

* Corresponding Author: Leilei Chen. Email:

(This article belongs to the Special Issue: Integration of Physical Simulation and Machine Learning in Digital Twin and Virtual Reality)

Computer Modeling in Engineering & Sciences 2024, 140(1), 1143-1163. https://doi.org/10.32604/cmes.2024.048549

Received 11 December 2023; Accepted 07 February 2024; Issue published 16 April 2024

Abstract

This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from 2D images. This approach reconstructs color and density fields from 2D images using Neural Radiance Field (NeRF) and improves image quality using frequency regularization. The NeRF model is obtained via joint training of multiple artificial neural networks, whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel. In addition, customized physics-informed neural network (PINN) with residual blocks and two-layer activation functions are utilized to input the density fields of the NeRF into Navier-Stokes equations and convection-diffusion equations to reconstruct the velocity field. The velocity uncertainties are also evaluated through ensemble learning. The effectiveness of the proposed algorithm is demonstrated through numerical examples. The present method is an important step towards downstream tasks such as reliability analysis and robust optimization in engineering design.

---

Keywords

---