  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.
