Thermochemically Constrained Multiscale Laplace Neural Operator to Learn Stiff Chemical Kinetics with Conditional Diffusion Model Sampling

Abstract

Stiff chemical kinetics is a major computational bottleneck in reacting-flow simulations, while data-driven solvers remain sensitive to training-state coverage and chemical dynamics. This work combines conditional diffusion sampling with a thermochemically constrained multiscale Laplace neural operator (TC-MLNO) for chemistry ODE integration. The diffusion model learns the equivalence-ratio-conditioned joint distribution of temperature and species from low-dimensional flame data, augmenting the state space without independent perturbations. TC-MLNO represents transient, non-periodic responses through pole-residue Laplace layers and assigns fast, medium, and slow species to separate branches. Thermochemical constraints are imposed through losses for mass and elemental conservation and heat release rate. The framework is evaluated in 1D premixed flames, a 2D developing jet, and a 3D turbulent burner flame. With equal-sized datasets, diffusion sampling reduces the 95th-percentile distance to the base flame manifold by up to 37.5% and the a posteriori full-species macro-average error by up to 92.7% versus random sampling, especially for minor species and radicals. TC-LNO yields smaller errors than the DeepONet baseline for 84.9% of retained modes and reduces the 95th-percentile error for the most attenuated modes from 0.372 to 0.081. In multidimensional flames, TC-MLNO better preserves reaction-zone locations, heat-release structures, and chemically sensitive species than DeepONet. Errors of representative radical and nitrogen-containing species in the 3D flame decrease by 88.0%-88.9%. Compared with direct CVODE integration, TC-MLNO reduces mean chemistry and total solution times by 90.1% and 62.6%, respectively. These results show that distribution-aware sampling and Laplace neural operator learning provide an accurate and efficient alternative for stiff chemical ODE integration.

Main text: 14 pages, 13 figures. Supplementary Materials: 3 pages, 3 figures