physics.chem-phMar 5, 2026

Particle-Guided Diffusion for Gas-Phase Reaction Kinetics

Authors: Andrew Millard, Henrik Pedersen

Organizations: Department of Computer and Information Science, Linköping University, Linköping, Sweden · Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden

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Abstract

Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply diffusion-based guided sampling to gas-phase chemical reactions by training on solutions of the advection-reaction-diffusion (ARD) equation across varying parameters. The method generates physically consistent concentration fields and accurately predicts outlet concentrations, including at unseen parameter values, demonstrating the potential of diffusion models for inference in reactive transport.

Figures & tables

MethodSpeciesGT FinalPred FinalRMSEMAE
 NO9.710×10−39.710\times 10^{-3}9.879×10−3±1.35×10−2\mathbf{9.879\times 10^{-3}}\pm 1.35\times 10^{-2}5.445×10−4±8.90×10−4\mathbf{5.445\times 10^{-4}}\pm 8.90\times 10^{-4}1.664×10−4±2.00×10−4\mathbf{1.664\times 10^{-4}}\pm 2.00\times 10^{-4}
SMCO34.942×10−34.942\times 10^{-3}5.093×10−3±8.68×10−3\mathbf{5.093\times 10^{-3}}\pm 8.68\times 10^{-3}5.517×10−4±9.52×10−4\mathbf{5.517\times 10^{-4}}\pm 9.52\times 10^{-4}1.694×10−4±1.98×10−4\mathbf{1.694\times 10^{-4}}\pm 1.98\times 10^{-4}
 NO22.464×10−22.464\times 10^{-2}2.447×10−2±1.50×10−2\mathbf{2.447\times 10^{-2}}\pm 1.50\times 10^{-2}6.361×10−4±8.18×10−4\mathbf{6.361\times 10^{-4}}\pm 8.18\times 10^{-4}2.322×10−4±1.92×10−4\mathbf{2.322\times 10^{-4}}\pm 1.92\times 10^{-4}
 NO9.710×10−39.710\times 10^{-3}7.020×10−3±9.51×10−37.020\times 10^{-3}\pm 9.51\times 10^{-3}4.430×10−3±2.73×10−34.430\times 10^{-3}\pm 2.73\times 10^{-3}1.681×10−3±1.19×10−31.681\times 10^{-3}\pm 1.19\times 10^{-3}
ODEO34.942×10−34.942\times 10^{-3}4.699×10−3±7.91×10−34.699\times 10^{-3}\pm 7.91\times 10^{-3}3.468×10−3±2.17×10−33.468\times 10^{-3}\pm 2.17\times 10^{-3}1.165×10−3±7.94×10−41.165\times 10^{-3}\pm 7.94\times 10^{-4}
 NO22.464×10−22.464\times 10^{-2}1.958×10−2±1.13×10−21.958\times 10^{-2}\pm 1.13\times 10^{-2}3.467×10−3±2.46×10−33.467\times 10^{-3}\pm 2.46\times 10^{-3}1.559×10−3±1.24×10−31.559\times 10^{-3}\pm 1.24\times 10^{-3}
Table 1: Outlet concentration summary averaged over common simulation-seed pairs for SMC and ODE methods. We report the mean ±\pm standard deviation for all metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and outlet concentrations of the chemical species at the final timestep (Pred Final). Best values per species are shown in bold (lowest RMSE/MAE and closest final prediction to GT). The RMSE and the MAE are the mean errors across all time steps.
Figure 1: Predicted species concentration at the outlet over time for an example simulation averaged over three seeds. The quantitative results for these simulations are given in Table 2 .
MethodSpeciesGT FinalPred FinalRMSEMAE
 NO1.89×10−21.89\times 10^{-2}1.90×10−2±1.96×10−41.90\times 10^{-2}\pm 1.96\times 10^{-4}1.58×10−4±3.38×10−51.58\times 10^{-4}\pm 3.38\times 10^{-5}8.17×10−5±1.24×10−58.17\times 10^{-5}\pm 1.24\times 10^{-5}
SMCO32.24×10−92.24\times 10^{-9}1.37×10−4±2.50×10−51.37\times 10^{-4}\pm 2.50\times 10^{-5}7.41×10−5±9.09×10−67.41\times 10^{-5}\pm 9.09\times 10^{-6}5.49×10−5±7.75×10−65.49\times 10^{-5}\pm 7.75\times 10^{-6}
 NO23.79×10−23.79\times 10^{-2}3.74×10−2±3.80×10−43.74\times 10^{-2}\pm 3.80\times 10^{-4}2.03×10−4±7.11×10−52.03\times 10^{-4}\pm 7.11\times 10^{-5}1.08×10−4±2.71×10−51.08\times 10^{-4}\pm 2.71\times 10^{-5}
 NO1.89×10−21.89\times 10^{-2}1.48×10−2±3.24×10−31.48\times 10^{-2}\pm 3.24\times 10^{-3}2.90×10−3±2.78×10−32.90\times 10^{-3}\pm 2.78\times 10^{-3}8.90×10−4±7.88×10−48.90\times 10^{-4}\pm 7.88\times 10^{-4}
ODEO32.24×10−92.24\times 10^{-9}1.70×10−4±1.18×10−41.70\times 10^{-4}\pm 1.18\times 10^{-4}1.29×10−3±1.06×10−31.29\times 10^{-3}\pm 1.06\times 10^{-3}2.73×10−4±2.09×10−42.73\times 10^{-4}\pm 2.09\times 10^{-4}
 NO23.79×10−23.79\times 10^{-2}2.94×10−2±6.91×10−32.94\times 10^{-2}\pm 6.91\times 10^{-3}2.81×10−3±1.63×10−32.81\times 10^{-3}\pm 1.63\times 10^{-3}1.03×10−3±6.25×10−41.03\times 10^{-3}\pm 6.25\times 10^{-4}
Table 2: Quantitative simulation results corresponding to Figures 1 . Parameter values are Uavg=0.093U_{\mathrm{avg}}=0.093 , D=6.43×10−6D=6.43\times 10^{-6} , κ=7.51×103\kappa=7.51\times 10^{3} .
Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2: Diagram of the experiment.
NobsN_{\text{obs}}SpeciesGT FinalPred FinalRMSEMAE
 NO1.89×10−21.89\times 10^{-2}1.90×10−21.90\times 10^{-2} ±\pm 2.48×10−52.48\times 10^{-5}1.95×10−41.95\times 10^{-4} ±\pm 6.80×10−56.80\times 10^{-5}1.02×10−41.02\times 10^{-4} ±\pm 2.24×10−52.24\times 10^{-5}
25O32.24×10−92.24\times 10^{-9}9.89×10−5\bm{9.89\times 10^{-5}} ±\pm 8.82×10−58.82\times 10^{-5}4.80×10−5\bm{4.80\times 10^{-5}} ±\pm 1.22×10−51.22\times 10^{-5}3.16×10−5\bm{3.16\times 10^{-5}} ±\pm 6.89×10−66.89\times 10^{-6}
 NO23.79×10−23.79\times 10^{-2}3.76×10−23.76\times 10^{-2} ±\pm 3.83×10−43.83\times 10^{-4}4.55×10−44.55\times 10^{-4} ±\pm 1.55×10−41.55\times 10^{-4}2.14×10−42.14\times 10^{-4} ±\pm 5.30×10−55.30\times 10^{-5}
 NO1.89×10−21.89\times 10^{-2}1.89×10−21.89\times 10^{-2} ±\pm 8.47×10−58.47\times 10^{-5}1.81×10−41.81\times 10^{-4} ±\pm 3.25×10−53.25\times 10^{-5}9.24×10−59.24\times 10^{-5} ±\pm 1.56×10−51.56\times 10^{-5}
50O32.24×10−92.24\times 10^{-9}1.24×10−41.24\times 10^{-4} ±\pm 2.11×10−52.11\times 10^{-5}5.53×10−55.53\times 10^{-5} ±\pm 5.30×10−65.30\times 10^{-6}4.05×10−54.05\times 10^{-5} ±\pm 4.34×10−64.34\times 10^{-6}
 NO23.79×10−23.79\times 10^{-2}3.77×10−23.77\times 10^{-2} ±\pm 9.47×10−59.47\times 10^{-5}3.46×10−43.46\times 10^{-4} ±\pm 5.85×10−55.85\times 10^{-5}1.65×10−41.65\times 10^{-4} ±\pm 1.95×10−51.95\times 10^{-5}
Appendix
Table 3: Ablation simulation results for differing numbers of observations inside the reactor when using the GEM proposal with an SMC framework. Mean ±\pm standard deviation are reported across metrics.
Figure 3: Change in the fraction of species present in the reactor over time.
Figure 4: Reconstruction fields and errors at different time points.
Figure 5: Reconstruction fields and errors at different time points (continued).
Figure 6: Reconstruction fields and errors at different time points (continued).
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