IDEA: Artificial neural network models for 11-species air properties at thermochemical equilibrium

Abstract

Accurate prediction of high-temperature air properties is essential in many aerodynamic applications under hypersonic flight conditions. Various curve-fit models using piecewise polynomial fittings have been commonly adopted to approximate equilibrium air properties at high temperatures. Several shortcomings including low accuracy, lack of diversity, and discontinuity at curve-fit boundary still remain, causing numerical troubles in computational procedures. To address the issues, IDEA, an open-source C++ library that enables fast and accurate computations of the equilibrium air properties and their first and second derivatives, is newly developed based on the artificial neural network (ANN). IDEA, which stands for the Infinitely Differentiable Equilibrium Air, predicts thermodynamic and transport properties of 11-species (N2, O2, N, O, NO, NO+, N+, O+, N++, O++, and e-) thermochemical equilibrium air at the temperature range up to 25,000 K and density range from 10-7 to 103 amagats. The training data is constructed from the kinetic molecular theory using the equilibrium constant method with the rigid-rotor, harmonic-oscillator model. As the name suggests, IDEA's models are infinitely differentiable in the application range; thus, they have enhanced convergence in computational fluid dynamics (CFD) when using gradient-based methods. Using a newly developed training process based on the Levenberg- Marquardt algorithm with weighted mean squared error loss, IDEA provides more accurate and diverse property models with much fewer parameters than previous piecewise polynomial fitting models. In addition, the proposed training method offers easy extensions to various property models with different species data. IDEA provides C interfaces that can be used for programs in various computer languages, such as C/C++, Fortran, Python, and MATLAB. IDEA's modeling routines are thread-safe, so they can be safely used for parallel programs without performance loss. The accuracy and enhanced convergence of IDEA is demonstrated via several high-speed flow computationsProgram summaryProgram title: IDEACPC library link to program files: https://doi .org /10 .17632 /84rhtfz9n2 .1Developers' repository link: https://github .com /HojunYouKr /IDEA Licensing provisions: BSD-3-ClauseProgramming language: C++11Nature of problem: Accurate prediction of equilibrium air properties is essential in many aerodynamic applications under hypersonic flight conditions. Direct calculation of air properties by the kinetic molecular theory requires time-consuming iterative methods to solve nonlinear equations of species concentrations. Various piecewise polynomial models have been developed to avoid such iterations. However, the regression error of the polynomial models requires improvement, and the lack of diversity of the polynomial models makes iterative computations inevitable, causing computational inefficiency. Furthermore, these polynomial models are not continuously differentiable, which deteriorates the convergence characteristics of computational fluid dynamics (CFD) solvers.Solution method: ANN is chosen to model the equilibrium properties of air owing to its excellent capability as a universal function approximator and better adaptability to a large dataset than kernel methods. The hyperbolic tangent activation function makes the ANN model infinitely differentiable, which enables to use a superlinear training process and thus improves convergence characteristics. The newly proposed superlinear training process based on the Levenberg-Marquardt algorithm with weighted mean squared error loss provides more accurate and diverse property models with much fewer parameters than the existing polynomial models. As a result, the proposed ANN model is completely free from iterative computations.& COPY; 2023 Elsevier B.V. All rights reserved.