the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Accelerating models for multiphase chemical kinetics through machine learning with polynomial chaos expansion and neural networks
Matteo Krüger
Aryeh Feinberg
Marcel Müller
Ulrich Pöschl
Ulrich K. Krieger
Abstract. The heterogeneous chemistry of atmospheric aerosols involves multiphase chemical kinetics that can be described by kinetic multi-layer models (KM) explicitly resolving mass transport and chemical reaction. However, KM are computationally too expensive to be used as sub-modules in large-scale atmospheric models, and the computational costs also limit their utility in inverse modelling approaches commonly used to infer aerosol kinetic parameters from laboratory studies. In this study, we show how machine learning methods can generate inexpensive surrogate models based on the kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB). We apply and compare two common and openly available methods for the generation of surrogate models, polynomial chaos expansion (PCE) with UQLab and neural networks (NN) through the Python package Keras. We show that the PCE method is well-suited to determine global sensitivity indices of the KM and demonstrate how inverse modelling applications can be enabled or accelerated with NN-suggested sampling. These qualities make them suitable supporting tools for laboratory work in the interpretation of data and design of future experiments. Overall, the KM surrogate models investigated in this study are fast, accurate, and robust, which suggests their applicability as sub-modules in large-scale atmospheric models.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(2380 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2380 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Thomas Berkemeier et al.
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-1093', Anonymous Referee #1, 04 Jan 2023
Berkemeier et al. present two surrogate model approaches, polynomial chaos expansion and neural networks, used to predict discrete reaction times of kinetic multi-layer models and used for sensitivity analysis and inverse modelling. The paper is well-organized, concise, and appropriate for GMD. I recommend its publication after addressing the comments below.
One general comment: It is not clear in a first read what the surrogate models are predicting (in other words, what the targets are). On a second read, it seems like the targets are the order of magnitudes of 3 different reaction times: the 90% reaction time, half-life, and 10% reaction time. Using these targets instead of concentration targets makes sense if the application is machine learning aided sampling rather than full model replacement. However, many readers (including myself) might initially assume that surrogate models replicate the output of their reference model, so this non-standard target should be addressed earlier on.
Specific comments
1. The methodology would be easier to follow if the output and purpose of the surrogate models was described early on. This could be done on line 5 of the abstract, for example “we show how machine learning methods can generate inexpensive surrogate models \add{to predict reaction times for}\remove{based on} the kinetic multi-layer model of…”, or something to an equivalent effect.
2. Not required, but a suggestion that might improve clarity: could the authors perhaps include a table for the 3 outputs, similar to Table 1 for the input parameters? This might help new readers understand the targets more easily.
3. There is existing recent work towards network surrogate models in aerosol applications for atmospheric chemistry and physics. Though I have no objection to the mention of applications outside the field, e.g. chemical engineering and materials science, the authors could include several relevant references to round out the discussion around line 60, which would help embed this work in recent literature on ML surrogate modelling for aerosol applications.
a. Surrogate model of MOSAIC, which includes heterogenous chemistry and mass transfer: https://doi.org/10.1029/2020JD032759
b. Mass-conserving surrogate model of mass transfer for bulk/surface partitioning: https://doi.org/10.5194/gmd-15-3417-2022
c. Physics-informed surrogate model of aerosol microphysics, specifically the M7 module: https://doi.org/10.1017/eds.2022.22.
Berkemeier et al. train surrogate models on a more granular kinetic multilayer model, for use in sampling rather than a solver / operator replacement (thus predicting a different output instead of concentration distributions). Inclusion of these more relevant references will allow the authors to make clear what the contribution of this paper is in the context of the field.
4. Line 65: “In the PCE approach, the full model is represented as an infinite series…” I would get rid of the word infinite here, or perhaps say “In the PCE approach, the full model can be approximated by a series…”. The PCE approach assumes the model can be represented as an infinite series, but is not applied in practice. This isn’t clearly stated until mention of truncation around line 136.
5. Figure 2: Are these correlation coefficients for just the log10 of half-life or for all reaction times, as line 205 suggests? Also, maybe “halflife” could be hyphenated to match the text? The inset for the laboratory-experiment relevant timescale is a nice addition.
Citation: https://doi.org/10.5194/egusphere-2022-1093-RC1 -
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
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AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
-
RC2: 'Comment on egusphere-2022-1093', Anonymous Referee #2, 19 Jan 2023
Review of Berkemeier et al.
Berkemeier et al. present work using neural networks and polynomial chaos expansion to emulate complex models of multiphase kinetics for atmospheric aerosols. They find that both techniques are suitable for emulation, and assess the benefits and drawbacks of each approach. In general, the work is well-presented, addresses an important topic, and provides a valuable contribution to the scientific literature. I have a few comments that I believe should be addressed before this paper is accepted for publication.
Motivation
The motivation of this work makes it challenging to understand exactly what the emulators are being used to emulate. This becomes clear on a more careful read, but I suggest the authors clarify for readability.
Emulator Performance
The authors demonstrate very good bulk performance of their emulators in predicting the target quantity. However, the error of the methods as a function of the input parameter space is important to assess (e.g., error as a function of initial gas phase concentration). If the error is largely independent of the input parameter space, a sentence clarifying this would suffice.
L54-56
Much work on NN in the atmospheric science has been done since 1998. I suggest improving the citations here.
L93
Were other normalization strategies explored (e.g., log-normal outputs)?
L190
These packages need citations.
Table A2
Some of these hyperparameters selected are at the upper boundary of the sampled parameter space. This suggests that additional exploration would benefit model performance. Particularly for the shallow NN number of neurons parameter.
Citation: https://doi.org/10.5194/egusphere-2022-1093-RC2 -
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
-
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
-
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1093', Anonymous Referee #1, 04 Jan 2023
Berkemeier et al. present two surrogate model approaches, polynomial chaos expansion and neural networks, used to predict discrete reaction times of kinetic multi-layer models and used for sensitivity analysis and inverse modelling. The paper is well-organized, concise, and appropriate for GMD. I recommend its publication after addressing the comments below.
One general comment: It is not clear in a first read what the surrogate models are predicting (in other words, what the targets are). On a second read, it seems like the targets are the order of magnitudes of 3 different reaction times: the 90% reaction time, half-life, and 10% reaction time. Using these targets instead of concentration targets makes sense if the application is machine learning aided sampling rather than full model replacement. However, many readers (including myself) might initially assume that surrogate models replicate the output of their reference model, so this non-standard target should be addressed earlier on.
Specific comments
1. The methodology would be easier to follow if the output and purpose of the surrogate models was described early on. This could be done on line 5 of the abstract, for example “we show how machine learning methods can generate inexpensive surrogate models \add{to predict reaction times for}\remove{based on} the kinetic multi-layer model of…”, or something to an equivalent effect.
2. Not required, but a suggestion that might improve clarity: could the authors perhaps include a table for the 3 outputs, similar to Table 1 for the input parameters? This might help new readers understand the targets more easily.
3. There is existing recent work towards network surrogate models in aerosol applications for atmospheric chemistry and physics. Though I have no objection to the mention of applications outside the field, e.g. chemical engineering and materials science, the authors could include several relevant references to round out the discussion around line 60, which would help embed this work in recent literature on ML surrogate modelling for aerosol applications.
a. Surrogate model of MOSAIC, which includes heterogenous chemistry and mass transfer: https://doi.org/10.1029/2020JD032759
b. Mass-conserving surrogate model of mass transfer for bulk/surface partitioning: https://doi.org/10.5194/gmd-15-3417-2022
c. Physics-informed surrogate model of aerosol microphysics, specifically the M7 module: https://doi.org/10.1017/eds.2022.22.
Berkemeier et al. train surrogate models on a more granular kinetic multilayer model, for use in sampling rather than a solver / operator replacement (thus predicting a different output instead of concentration distributions). Inclusion of these more relevant references will allow the authors to make clear what the contribution of this paper is in the context of the field.
4. Line 65: “In the PCE approach, the full model is represented as an infinite series…” I would get rid of the word infinite here, or perhaps say “In the PCE approach, the full model can be approximated by a series…”. The PCE approach assumes the model can be represented as an infinite series, but is not applied in practice. This isn’t clearly stated until mention of truncation around line 136.
5. Figure 2: Are these correlation coefficients for just the log10 of half-life or for all reaction times, as line 205 suggests? Also, maybe “halflife” could be hyphenated to match the text? The inset for the laboratory-experiment relevant timescale is a nice addition.
Citation: https://doi.org/10.5194/egusphere-2022-1093-RC1 -
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
-
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
-
RC2: 'Comment on egusphere-2022-1093', Anonymous Referee #2, 19 Jan 2023
Review of Berkemeier et al.
Berkemeier et al. present work using neural networks and polynomial chaos expansion to emulate complex models of multiphase kinetics for atmospheric aerosols. They find that both techniques are suitable for emulation, and assess the benefits and drawbacks of each approach. In general, the work is well-presented, addresses an important topic, and provides a valuable contribution to the scientific literature. I have a few comments that I believe should be addressed before this paper is accepted for publication.
Motivation
The motivation of this work makes it challenging to understand exactly what the emulators are being used to emulate. This becomes clear on a more careful read, but I suggest the authors clarify for readability.
Emulator Performance
The authors demonstrate very good bulk performance of their emulators in predicting the target quantity. However, the error of the methods as a function of the input parameter space is important to assess (e.g., error as a function of initial gas phase concentration). If the error is largely independent of the input parameter space, a sentence clarifying this would suffice.
L54-56
Much work on NN in the atmospheric science has been done since 1998. I suggest improving the citations here.
L93
Were other normalization strategies explored (e.g., log-normal outputs)?
L190
These packages need citations.
Table A2
Some of these hyperparameters selected are at the upper boundary of the sampled parameter space. This suggests that additional exploration would benefit model performance. Particularly for the shallow NN number of neurons parameter.
Citation: https://doi.org/10.5194/egusphere-2022-1093-RC2 -
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
-
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
-
AC1: 'Response to reviewers of egusphere-2022-1093', Thomas Berkemeier, 15 Feb 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1093/egusphere-2022-1093-AC1-supplement.pdf
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Journal article(s) based on this preprint
Thomas Berkemeier et al.
Thomas Berkemeier et al.
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