mlsanityData to 7 Oct 2026

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

arXiv 2210.15799 ↗First posted 27 Oct 2022physics.comp-ph cs.LGcited by 6

Not on the map. Why?

Abstract (arXiv)

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-D scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-D shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 29 of its 138 references that are in the map. First posted on arXiv 27 Oct 2022.

Builds on

29 of 138 references.

References · 29

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  6. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  7. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  8. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  9. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 173
  10. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 144
  11. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  12. 2022Physics-Informed Deep Neural Operator Networkscited by 110
17 more
  1. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  2. 2022Learning Operators with Coupled Attentioncited by 88
  3. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  4. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  5. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  6. 2020Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domainscited by 78
  7. 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
  8. 2019Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamicscited by 45
  9. 2022Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Networkcited by 45
  10. 2020Hierarchical Deep Learning of Multiscale Differential Equation Time-Stepperscited by 37
  11. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  12. 2019Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problemscited by 31
  13. 2022Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solverscited by 12
  14. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12
  15. 2021Generalized Joint Probability Density Function Formulation inTurbulent Combustion using DeepONetcited by 8
  16. 2022Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operatorscited by 5
  17. 2021Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representationscited by 2

Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 2; 2025: 2.

6 papers.

  1. 2023Rethinking materials simulations: Blending direct numerical simulations with neural operatorscited by 25
  2. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  3. 2024Neural Parameter Regression for Explicit Representations of PDE Solution Operatorscited by 1
  4. 2024Adaptive Error-Bounded Hierarchical Matrices for Efficient Neural Network Compressioncited by 0
  5. 2025Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Datacited by 0
  6. 2025Physics-Based Machine Learning Closures and Wall Models for Hypersonic Transition-Continuum Boundary Layer Predictionscited by 0