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1. Interpretation of High-Dimensional Linear Regression: Effects of Nullspace and Regularization Demonstrated on Battery Data

Author

Schaeffer, Joachim, Lenz, Eric, Chueh, William C., Bazant, Martin Z., Findeisen, Rolf, and Braatz, Richard D.

Subjects
Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Applications, Statistics - Methodology, 62J07, 62P99, I.2.6
Abstract

High-dimensional linear regression is important in many scientific fields. This article considers discrete measured data of underlying smooth latent processes, as is often obtained from chemical or biological systems. Interpretation in high dimensions is challenging because the nullspace and its interplay with regularization shapes regression coefficients. The data's nullspace contains all coefficients that satisfy $\mathbf{Xw}=\mathbf{0}$, thus allowing very different coefficients to yield identical predictions. We developed an optimization formulation to compare regression coefficients and coefficients obtained by physical engineering knowledge to understand which part of the coefficient differences are close to the nullspace. This nullspace method is tested on a synthetic example and lithium-ion battery data. The case studies show that regularization and z-scoring are design choices that, if chosen corresponding to prior physical knowledge, lead to interpretable regression results. Otherwise, the combination of the nullspace and regularization hinders interpretability and can make it impossible to obtain regression coefficients close to the true coefficients when there is a true underlying linear model. Furthermore, we demonstrate that regression methods that do not produce coefficients orthogonal to the nullspace, such as fused lasso, can improve interpretability. In conclusion, the insights gained from the nullspace perspective help to make informed design choices for building regression models on high-dimensional data and reasoning about potential underlying linear models, which are important for system optimization and improving scientific understanding., Comment: Manuscript: 14 pages, 7 figures; Supplementary Information: 4 pages, 2 figures; Code available: https://github.com/JoachimSchaeffer/HDRegAnalytics

Published
2023
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30. Proton-coupled electron transfer at SOFC electrodes.

Author

Williams, Nicholas J., Warburton, Robert E., Seymour, Ieuan D., Cohen, Alexander E., Bazant, Martin Z., and Skinner, Stephen J.

Subjects
CHARGE exchange, SOLID oxide fuel cells, QUANTUM tunneling, ACTIVATION energy, SURFACE potential, TRANSITION state theory (Chemistry)
Abstract

Understanding the charge transfer processes at solid oxide fuel cell (SOFC) electrodes is critical to designing more efficient and robust materials. Activation losses at SOFC electrodes have been widely attributed to the ambipolar migration of charges at the mixed ionic–electronic conductor–gas interface. Empirical Butler–Volmer kinetics based on the transition state theory is often used to model the current–voltage relationship, where charged particles transfer classically over an energy barrier. However, the hydrogen oxidation/water electrolysis reaction H2(g) + O2− ⇌ H2O(g) + 2e− must be modeled through concerted electron and proton tunneling events, where we unify the theory of the electrostatic surface potential with proton-coupled electron transfer kinetics. We derive a framework for the reaction rate that depends on the electrostatic surface potential, adsorbate dipole moment, the electronic structure of the electron donor/acceptor, and vibronic states of the hydrogen species. This theory was used to study the current–voltage characteristics of the Ni/gadolinium-doped ceria electrode in H2/H2O(g), where we find excellent validation of this novel model. These results yield the first reported quantification of the solvent reorganization energy for an SOFC material and suggest that the three-phase boundary mechanism is the dominant pathway for charge transfer at cermet electrodes. [ABSTRACT FROM AUTHOR]

Published
2023
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41. Electric field induced associations in the double layer of salt-in-ionic-liquid electrolytes.

Author

Markiewitz, Daniel M., Goodwin, Zachary A. H., McEldrew, Michael, Pedro de Souza, J., Zhang, Xuhui, Espinosa-Marzal, Rosa M., and Bazant, Martin Z.

Abstract

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However, at large negative voltages, which are strong enough to break the alkali metal cation–anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes more aggregated while screening the electrode charge from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements. [ABSTRACT FROM AUTHOR]

Published
2024
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42. Gelation, clustering, and crowding in the electrical double layer of ionic liquids.

Author

Goodwin, Zachary A. H., McEldrew, Michael, Pedro de Souza, J., Bazant, Martin Z., and Kornyshev, Alexei A.

Subjects
IONIC liquids, GELATION, POLYMER colloids, SUPERCAPACITORS
Abstract

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. [J. Phys. Chem. B 125, 2677 (2021)] developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible (Cayley tree) clusters and a percolating ionic network (gel). Here, we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition. [ABSTRACT FROM AUTHOR]

Published
2022
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48. Polar liquids at charged interfaces: A dipolar shell theory.

Author

de Souza, J.Pedro, Kornyshev, Alexei A., and Bazant, Martin Z.

Subjects
MOLECULAR dynamics, AQUEOUS electrolytes, LIQUIDS, HYDRATION, SOLUTION (Chemistry)
Abstract

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface. [ABSTRACT FROM AUTHOR]

Published
2022
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