Source-linked AI summary
Simulation of multi-species flow and heat transfer using physics-informed neural networks
Ryno Laubscher
TL;DR
The paper evaluates PINNs for steady-state multi-species flow and heat transfer, where coupled momentum, species and energy transport are compared using single-network and segregated-network architectures against OpenFOAM CFD. It finds that the segregated approach lowers losses and better preserves species conservation, while also supporting parameterised predictions for varying water-vapour inlet velocities.
Problem
The paper examines the limited prior investigation of PINNs for simultaneous mass, momentum, species and energy transport and segregated physics-specific PINNs.
Method
The study compares single- and segregated-network PINNs for a 2D dry-air humidification duct, using variable fluid properties and OpenFOAM CFD for reference.
Results
The segregated PINN approach produced losses 62% lower on average than the single-network approach and successfully resolved species conservation where the single network struggled.
Takeaways & Limitations
The segregated PINN approach produced parameterised predictions of velocity, temperature and water mass fraction for various water-vapour inlet velocities.
Takeaways & Limitations
The models assume an incompressible ideal-gas mixture whose density depends only on local temperature and mixture composition.
Abstract
from arXiv · showhide
In the present work, single- and segregated-network PINN architectures are applied to predict momentum, species and temperature distributions of a dry air humidification problem in a simple 2D rectangular domain. The created PINN models account for variable fluid properties, species- and heat-diffusion and convection. Both the mentioned PINN architectures were trained using different hyperparameter settings, such as network width and depth to find the best-performing configuration. It is shown that the segregated-network PINN approach results in on-average 62% lower losses when compared to the single-network PINN architecture for the given problem. Furthermore, the single-network variant struggled to ensure species mass conservation in different areas of the computational domain, whereas, the segregated approach successfully maintained species conservation. The PINN predicted velocity, temperature and species profiles for a given set of boundary conditions were compared to results generated using OpenFOAM software. Both the single- and segregated-network PINN models produced accurate results for temperature and velocity profiles, with average percentage difference relative to the CFD results of approximately 7.5% for velocity and 8% for temperature. The mean error percentages for the species mass fractions are 9\% for the single-network model and 1.5% for the segregated-network approach. To showcase the applicability of PINNs for surrogate modelling of multi-species problems, a parameterised version of the segregated-network PINN is trained which could produce results for different water vapour inlet velocities. The normalised mean absolute percentage errors, relative to the OpenFOAM results, across three predicted cases for velocity and temperature are approximately 7.5% and 2.4% for water vapour mass fraction.
1 Introduction
This work evaluates PINNs for steady-state multi-species flow and heat transfer, comparing single-network and segregated-network architectures against CFD simulations. It also investigates how network hyperparameters affect losses and addresses a previously unexplored segregated approach for coupled transport.
- PINNs are motivated as computationally efficient surrogate models for applications including design optimisation, multi-scale simulation, inverse modelling and fast performance-monitoring simulations.
- The study evaluates PINNs for steady-state momentum, species and energy equations in a 2D dry-air humidification duct, using OpenFOAM CFD as the comparison baseline.
- Two architectures are compared: PINN-1 uses one network for all physics, while PINN-3 uses three networks that exchange relevant solution variables during training.
- The models are trained across different network depths, widths and sampling densities to examine their effects on achievable combined loss values.
- The paper addresses an identified gap because prior work had not investigated PINNs for simultaneous mass, momentum, species and energy transport or segregated physics-specific PINNs.
2 Material and methods
The study formulates a steady-state 2D PINN framework for coupled mass, momentum, species, and energy transport in a humidification duct. It uses normalized physics equations, automatic differentiation, residual and boundary losses, variable fluid properties, and a single-network architecture for simultaneous prediction.
- PINN formulation: MLP networks predict transported fields from spatial coordinates, including species mass fractions, velocity, and temperature.The network inputs are coordinates within the computational domain, and its outputs approximate selected PDE solution variables.
- PINN formulation: Automatic differentiation evaluates differential operators from network outputs to construct PDE residuals for advection, diffusion, and source terms.The operator represents linear and nonlinear PDE quantities, while network gradients are obtained through the computational graph.
- Training losses: The combined loss minimizes PDE residuals and boundary-condition errors across internal and boundary sampling points.Residual losses are evaluated inside the domain, while boundary losses impose inlet, outlet, and wall conditions.
- Case study: The case study simulates water-vapour propagation into dry air in a 0.5 × 0.1 m rectangular duct with specified inlet, outlet, and wall conditions.The governing system includes steady-state mass, momentum, species, and energy transport equations and is compared with OpenFOAM finite-volume results.
- Case study: The models assume an incompressible ideal-gas mixture whose density depends on local temperature and composition, with constant conductivity and viscosity.The mixture also uses a mass-weighted heat capacity and a constant dilute-approximation molecular diffusion coefficient.
- Normalization and constraints: Normalization balances disparate momentum, heat, and species scales before loss minimization, while an additional residual enforces species mass-fraction summation.The temperature range is 300–600 K and the velocity range is 0–0.1 m/s; the added constraint requires the species fractions to sum to unity.
- Network architecture: PINN-1 uses one MLP to output 18 physical quantities and updates variable fluid properties from predicted temperature and composition during training.The single optimizer minimizes the combined loss formed from predictions at internal points and boundaries.
3 Results and discussion
The study compares PINN-1 and segregated PINN-3 architectures across network, depth, sampling-density, and CFD-validation experiments. PINN-3 generally achieves lower losses and more accurate species predictions, while PINN-1 can perform competitively for velocity and temperature under adjusted settings.
- Hyperparameter search: A coarse grid search varied hidden-layer width, network depth, and domain sampling density while comparing PINN-1 and PINN-3 configurations.Training parameters were kept approximately comparable between architectures.
- Network depth: 68%, 78%, and 86% were the average percentage differences favoring PINN-3 over PINN-1 for momentum, energy, and species losses, respectively.The 7-layer PINN-3 had the lowest species and energy losses, while the 5-layer variant had the lowest momentum loss; the 5-layer model was selected because the deeper-model advantage was small.
- Sampling density: 15,000 sampling points produced the best PINN-3 combined losses, whereas PINN-1 achieved its best results with 30,000 coordinate points.The selected comparison used PINN-1 (5 × 86) trained with 30,000 points and PINN-3 (5 × 50) trained with 15,000 points.
- CFD comparison: 14.8% and 5.6% were PINN-1 X- and Y-velocity NMAPEs, compared with 8.2% and 2.5% for PINN-3.PINN-3 agreed well with CFD, while PINN-1 underpredicted the velocity profiles.
- CFD comparison: Reducing PINN-1 width to 51 neurons lowered its X- and Y-velocity NMAPEs to 7.2% and 1.75% and its temperature NMAPE to 6.5%.Its H2O and O2 errors remained 6.0% and 11.4%, higher than PINN-3, and summed mass fractions still were not consistently 1.
- Parameterised model: 7.7%, 7.8%, and 2.43% were the average velocity, temperature, and water-mass-fraction NMAPEs across three parameterised PINN-3 cases.The parameterised model added water-vapour boundary velocity as an input and was trained over 0.0001 → 0.01 m/s.
4 Conclusions
The study compares single-network and segregated-network PINNs for 2D multi-species flow and heat transfer, finding advantages for the segregated approach in loss reduction, species conservation, and parameterized prediction.
- 62% lower average losses were obtained with PINN-3 than with PINN-1 across the trained models.The models varied in neural-network architectures and sampling densities.
- PINN-1 adequately resolved momentum and energy equations but struggled with species mass transport, whereas PINN-3 successfully resolved the physics equations.
- PINN-3 predicted velocity, temperature, and water mass fraction distributions for various water-vapour inlet velocities.The inlet velocity was provided as an additional network input for the surrogate model.
- PINN-3 is presented as an attractive methodology when more than 10 solution variables can be grouped into physics categories.The cited categories are species and energy transport.
- Future work will extend the segregated-network approach to reactive flows, particularly combustion, and add dynamic loss-function weighting.