# FlamePINN-1D: Physics-informed neural networks to solve forward and inverse problems of 1D laminar flames

arXiv: https://arxiv.org/abs/2406.09071 · HTML: https://mlsanity.com/paper/2406.09071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 84 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network](https://mlsanity.com/paper/2002.09062/) (2020)
- [ChemNODE: A Neural Ordinary Differential Equations Approach for Chemical Kinetics Solvers](https://mlsanity.com/paper/2101.04749/) (2020)
- [Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding](https://mlsanity.com/paper/2306.00230/) (2023)
- [Data-assisted combustion simulations with dynamic submodel assignment using random forests](https://mlsanity.com/paper/2009.04023/) (2020)
- [A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics](https://mlsanity.com/paper/2201.03549/) (2022)
- [An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure](https://mlsanity.com/paper/2005.09747/) (2020)

## Built on by (most cited first, 1 of 1)

- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)

## Abstract (arXiv)

Given the existence of various forward and inverse problems in combustion studies and applications that necessitate distinct methods for resolution, a framework to solve them in a unified way is critically needed. A promising approach is the integration of machine learning methods with governing equations of combustion systems, which exhibits superior generality and few-shot learning ability compared to purely data-driven methods. In this work, the FlamePINN-1D framework is proposed to solve the forward and inverse problems of 1D laminar flames based on physics-informed neural networks. Three cases with increasing complexity have been tested: Case 1 are freely-propagating premixed (FPP) flames with simplified physical models, while Case 2 and Case 3 are FPP and counterflow premixed (CFP) flames with detailed models, respectively. For forward problems, FlamePINN-1D aims to solve the flame fields and infer the unknown eigenvalues (such as laminar flame speeds) under the constraints of governing equations and boundary conditions. For inverse problems, FlamePINN-1D aims to reconstruct the continuous fields and infer the unknown parameters (such as transport and chemical kinetics parameters) from noisy sparse observations of the flame. Our results strongly validate these capabilities of FlamePINN-1D across various flames and working conditions. Compared to traditional methods, FlamePINN-1D is differentiable and mesh-free, exhibits no discretization errors, and is easier to implement for inverse problems. The inverse problem results also indicate the possibility of optimizing chemical mechanisms from measurements of laboratory 1D flames. Furthermore, some proposed strategies, such as hard constraints and thin-layer normalization, are proven to be essential for the robust learning of FlamePINN-1D. The code for this paper is partially available at https://github.com/CAME-THU/FlamePINN-1D.