# Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows

arXiv: https://arxiv.org/abs/2105.03332 · HTML: https://mlsanity.com/paper/2105.03332/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 56 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 15 of 15)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [The role of artificial intelligence in achieving the Sustainable Development Goals](https://mlsanity.com/paper/1905.00501/) (2019)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2002.03014/) (2020)
- [Finite Volume Neural Network: Modeling Subsurface Contaminant Transport](https://mlsanity.com/paper/2104.06010/) (2021)
- [On Vectorization of Deep Convolutional Neural Networks for Vision Tasks](https://mlsanity.com/paper/1501.07338/) (2015)
- [A Baseline Model for Software Effort Estimation](https://mlsanity.com/paper/2102.02933/) (2021)

## Built on by (most cited first, 12 of 12)

- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning](https://mlsanity.com/paper/2206.06817/) (2022)
- [Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and quality](https://mlsanity.com/paper/2407.17822/) (2024)
- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [Model-Agnostic AI Framework with Explicit Time Integration for Long-Term Fluid Dynamics Prediction](https://mlsanity.com/paper/2412.05657/) (2024)
- [Comparison of CNN-based deep learning architectures for unsteady CFD acceleration on small datasets](https://mlsanity.com/paper/2502.06837/) (2025)
- [Node Assigned physics-informed neural networks for thermal-hydraulic system simulation: CVH/FL module](https://mlsanity.com/paper/2504.16447/) (2025)
- [SPINN: An Optimal Self-Supervised Physics-Informed Neural Network Framework](https://mlsanity.com/paper/2509.05886/) (2025)
- [Coupling Machine Learning Local Predictions with a Computational Fluid Dynamics Solver to Accelerate Transient Buoyant Plume Simulations](https://mlsanity.com/paper/2409.07175/) (2024)
- [Physics-Informed Machine Learning Regulated by Finite Element Analysis for Simulation Acceleration of Melt Pool Dynamics in Laser Powder Bed Fusion](https://mlsanity.com/paper/2506.20537/) (2025)
- [A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation](https://mlsanity.com/paper/2604.02663/) (2026)
- [Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning](https://mlsanity.com/paper/2605.05217/) (2026)

## Abstract (arXiv)

Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks (CNNs) specialized in image processing in flow field prediction has been studied, but the need to develop a neural netweork design fitted for CFD is recently emerged. In this study, a neural network model introducing the finite volume method (FVM) with a unique network architecture and physics-informed loss function was developed to accelerate CFD simulations. The developed network model, considering the nature of the CFD flow field where the identical governing equations are applied to all grids, can predict the future fields with only two previous fields unlike the CNNs requiring many field images (>10,000). The performance of this baseline model was evaluated using CFD time series data from non-reacting flow and reacting flow simulation; counterflow and hydrogen flame with 20 detailed chemistries. Consequently, we demonstrated that (1) the FVM-based network architecture provided improved accuracy of multistep time series prediction compared to the previous MLP model (2) the physic-informed loss function prevented non-physical overfitting problem and ultimately reduced the error in time series prediction (3) observing the calculated residuals in an unsupervised manner could indirectly estimate the network accuracy. Additionally, under the reacting flow dataset, the computational speed of this network model was measured to be about 10 times faster than that of the CFD solver.