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

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.

💡 Research Summary

The paper addresses the challenge of efficiently exploring the high‑dimensional design space of gas‑diffusion electrodes (GDEs) for electrochemical CO₂ reduction, a technology that could store renewable electricity in chemical fuels. The authors propose a physics‑based, data‑driven modeling framework that integrates a differentiable one‑dimensional continuum model of the cathode with machine‑learning components to infer latent parameters and quantify predictive uncertainty.

Core Physical Model
The baseline is the analytical model of Blake et al. (2021), which describes CO₂ dissolution, diffusion, and reaction within the porous catalyst layer. The model is implemented in PyTorch, making it fully differentiable, and extended to multi‑product reactions (H₂, CO, C₂H₄) using Tafel kinetics with first‑order dependence on local reactant concentrations. The model takes as inputs the cathode voltage (or, in practice, the imposed current) and a set of electrode‑specific parameters (porosity ε, particle radius r, effective diffusion coefficient K_dl, and surface coverage fractions θ_i).

Latent‑Parameter Inference
Many of the required parameters cannot be measured directly in the automated laboratory. To estimate them, the authors train a multilayer perceptron (MLP) with architecture