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A physics-based data-driven model for CO$_2$ gas diffusion electrodes to drive automated laboratories

Ivan Grega, Félix Therrien, Abhishek Soni, Karry Ocean, Kevan Dettelbach, Ribwar Ahmadi, Mehrdad Mokhtari, Curtis P. Berlinguette, Yoshua Bengio

TL;DR

This work tackles the optimization of gas diffusion electrodes for CO$_2$ electroreduction under automated lab conditions by integrating a differentiable, physics-based 1D cathode model with data-driven latent parameter inference into a Gaussian process surrogate. By accommodating multi-product pathways (CO and C$_2$H$_4$) through Tafel-type kinetics and surface-fraction dynamics, the approach enables uncertainty-aware Bayesian optimization. Latent microstructural and kinetic parameters are inferred from AdaCarbon data, yielding interpretable ranges and insights into Cu- versus Ag-rich behavior. Simulated pool-based active learning demonstrates a roughly 3× efficiency gain over random sampling, highlighting the method’s potential to guide autonomous experiments in electrode design. Overall, the framework advances scalable, interpretable optimization of CO$_2$ reduction devices and paves the way for autonomous laboratories to iteratively improve GDE performance.

Abstract

The electrochemical reduction of atmospheric CO$_2$ into high-energy molecules with renewable energy is a promising avenue for energy storage that can take advantage of existing infrastructure especially in areas where sustainable alternatives to fossil fuels do not exist. Automated laboratories are currently being developed and used to optimize the composition and operating conditions of gas diffusion electrodes (GDEs), the device in which this reaction takes place. Improving the efficiency of GDEs is crucial for this technology to become viable. Here we present a modeling framework to efficiently explore the high-dimensional parameter space of GDE designs in an active learning context. At the core of the framework is an uncertainty-aware physics model calibrated with experimental data. The model has the flexibility to capture various input parameter spaces and any carbon products which can be modeled with Tafel kinetics. It is interpretable, and a Gaussian process layer can capture deviations of real data from the function space of the physical model itself. We deploy the model in a simulated active learning setup with real electrochemical data gathered by the AdaCarbon automated laboratory and show that it can be used to efficiently traverse the multi-dimensional parameter space.

A physics-based data-driven model for CO$_2$ gas diffusion electrodes to drive automated laboratories

TL;DR

This work tackles the optimization of gas diffusion electrodes for CO electroreduction under automated lab conditions by integrating a differentiable, physics-based 1D cathode model with data-driven latent parameter inference into a Gaussian process surrogate. By accommodating multi-product pathways (CO and CH) through Tafel-type kinetics and surface-fraction dynamics, the approach enables uncertainty-aware Bayesian optimization. Latent microstructural and kinetic parameters are inferred from AdaCarbon data, yielding interpretable ranges and insights into Cu- versus Ag-rich behavior. Simulated pool-based active learning demonstrates a roughly 3× efficiency gain over random sampling, highlighting the method’s potential to guide autonomous experiments in electrode design. Overall, the framework advances scalable, interpretable optimization of CO reduction devices and paves the way for autonomous laboratories to iteratively improve GDE performance.

Abstract

The electrochemical reduction of atmospheric CO into high-energy molecules with renewable energy is a promising avenue for energy storage that can take advantage of existing infrastructure especially in areas where sustainable alternatives to fossil fuels do not exist. Automated laboratories are currently being developed and used to optimize the composition and operating conditions of gas diffusion electrodes (GDEs), the device in which this reaction takes place. Improving the efficiency of GDEs is crucial for this technology to become viable. Here we present a modeling framework to efficiently explore the high-dimensional parameter space of GDE designs in an active learning context. At the core of the framework is an uncertainty-aware physics model calibrated with experimental data. The model has the flexibility to capture various input parameter spaces and any carbon products which can be modeled with Tafel kinetics. It is interpretable, and a Gaussian process layer can capture deviations of real data from the function space of the physical model itself. We deploy the model in a simulated active learning setup with real electrochemical data gathered by the AdaCarbon automated laboratory and show that it can be used to efficiently traverse the multi-dimensional parameter space.

Paper Structure

This paper contains 16 sections, 4 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Data structure and model inputs
  4. Differentiable inverse solver
  5. Uncertainty-aware model
  6. Results
  7. Uncertainty-aware predictions
  8. Interpretability of the model
  9. Simulated pool-based active learning
  10. Conclusion
  11. Appendix
  12. Sensitivity analysis
  13. Details of the physics model
  14. Physical constants
  15. Calibration of model ensembles
  16. ...and 1 more sections

Figures (5)

  • Figure 1: a) Schematic of the analytical model of the cathode. $\mathrm{CO_2}$ dissolves in the electrolyte as it enters the porous catalyst layer. The concentration profile of $\mathrm{CO_2}$$(c/c_0)$ is indicated on the schematic. Gaseous reaction products leave the system while other molecules and ions are dissolved in the electrolyte and in equilibrium. b) The analytical model is embedded in a data-driven framework (ML-Ph) where non-observable parameters are inferred from the data. c) The ML-Ph model is used as the mean function of a Gaussian process to enable uncertainty-aware predictions.
  • Figure 2: a,b) Parity plots over test set for Faradaic efficiency of ethylene and CO, respectively for the GP+Ph model. Error bars are $\pm \sigma$. Colors represent independent trials in 5-fold cross-validation. c) Maximum FE in the training pool as a function of step number in simulated active learning.
  • Figure 3: a,b) Histograms of inferred particle radius $r$ and porosity $\varepsilon$ for our dataset. c) Electrode reaction kinetics parameters $\alpha$ and $i^*$. Vertical bars show ranges of values reported in the literature lees2022 on Cu substrates. Red stars show values inferred for our dataset (mixture of Cu and Ag substrates). d) Faradaic efficiencies and surface coverage parameters $\theta_i$ for a virtual $x_\mathrm{Ag}$ sweep. Shaded bands indicate dropout-enabled variance gal2016dropout.
  • Figure 4: a) Dependence of selected quantities on half-cell voltage $V_{\mathrm{RHE}}$. b) Sensitivity of ethylene Faradaic efficiency to model parameters.
  • Figure 5: Hyperparameter exploration of model ensembles. Test loss and test negative log likelihood (NLL) for various data fractions and numbers of models.