Physics-based Machine Learning Discovered Nano-circuitry for Nonlinear Ion Transport in Nanoporous Electrodes

Aug 5, 2026

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Confined ion transport plays a central role in nanoporous ionic systems, yet mechanistic prediction of electrical characteristics remains difficult because conventional electrical circuit models are separated from the underlying physical chemistry. This work demonstrates that interpretable machine learning can bridge the gap by performing equation discovery from modified Poisson-Nernst-Planck simulation results, revealing anomalous diffusion–migration coupling. The resulting physics-based nano-circuitry yields physical insights into confined ion dynamics and explains non-ideal cyclic voltammetry behavior in nanoporous electrodes.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Abstract

Introduction

Challenges of conventional circuit models for nonlinear ion transport

Bottom-up construction of physics-based circuit elements

Methods

Conventional circuit modeling and Drude-based assumptions

Role of diffusion–migration interplay

Physics-based Machine Learning Discovered Nano-circuitry for Nonlinear Ion Transport in Nanoporous Electrodes Hualin Zhan1,2, Richard Sandberg3, Fan Feng3, Qinghua Liang1, Ke Xie1, Lianhai Zu1, Dan Li1, *, Jefferson Zhe Liu3, * 1 Department of Chemical Engineering, The University of Melbourne, VIC 3010, Australia 2 School of Engineering, The Australian National University, ACT 2601, Australia 3 Department of Mechanical Engineering, The University of Melbourne, VIC 3010, Australia Corresponding Author Dan Li: [dan.li1@unimelb.edu.au](dan.li1@unimelb.edu.au) Jefferson Zhe Liu: [zhe.liu@unimelb.edu.au](zhe.liu@unimelb.edu.au) ABSTRACT Confined ion transport is involved in nanoporous ionic systems. However, it is challenging to mechanistically predict its electrical characteristics for rational system design and performance evaluation using electrical circuit model due to the gap between the circuit theory and the underlying physical chemistry. Here we demonstrate that machine learning can bridge this gap and produce physics-based nano-circuitry, based on equation discovery from the modified Poisson-Nernst-Planck simulation results where an anomalous constructive diffusion-migration interplay of confined ions is unveiled. This bridging technique allows us to gain physical insights of ion dynamics in nanoporous electrodes, such as the non-ideal cyclic voltammetry. KEYWORDS nanoporous, confined ion dynamics, physics-based machine learning, circuit model, modified Poisson-Nernst-Planck theory Introduction Understanding and manipulation of ion transport and storage in nanoporous electrodes are essential to the development of ionic systems for applications including electrical energy storage, capacitive deionization, ionic circuits, and neuron stimulation 1-5. While the physicochemical mechanism of ion transport and storage can be understood by molecular dynamics and continuum-level simulations, experimental interpretation and design of highperformance systems are heavily assisted by electrical models6-12. As the electrical response of ionic systems is generally measured at the system level, circuit models can be constructed for the whole system to interpret or predict the results if all the charge transport processes involved can be justifiably represented as appropriate electrical elements. A common example is the transmission line model for porous materials where the electrical signal applied between the parallelly aligned electrical double layer and the in-pore surface is analogous to that between two parallel transmission lines 13, 14 . Due to the straightforward implementation, electrical circuit model allows highly efficient prediction of system performance, straightforward application of practical electrical input, and direct interfacing between ionic systems and external electronic circuits for various applications 15, 16. Numerous theoretical and experimental studies have shown that ions in nanoporous electrodes can behave differently from that in the open surface and often give rise to nonlinear dynamics17- 19. While these discoveries open up new opportunities for design of future generations of ionic systems, the conventional circuit models used for the system-level prediction have difficulty tackling nonlinear ion transport phenomena due to the complexity in describing the diffusion part of ion transport 17, 20. This difficulty, along with the notorious reputation of circuit models in insufficient validation of the physicochemical processes of ions, substantially hinders further exploration of circuit-based rational design and analysis of ionic systems6, 7, 10, 17, 21. This difficulty results from the fundamental gap between the electrical origin of circuit models and the physicochemical foundation of ionic systems, particularly when nanoporous electrodes are involved 8, 17. In nanoporous electrodes, the electrode-electrolyte interface region extends from the exterior surface of the electrod

FAQs

Why is it challenging to predict electrical characteristics of confined ion transport in nanoporous electrodes using traditional circuit models?

Because conventional circuit theory is not directly grounded in the physicochemical processes of ion transport, especially when nonlinear diffusion behavior and confined electrode–electrolyte interfaces are involved.

How does the proposed physics-based machine learning approach construct nano-circuitry?

It discovers governing equations from modified Poisson-Nernst-Planck (mPNP) simulation results, capturing the anomalous constructive coupling between diffusion and migration.

What physical insights does the resulting nano-circuitry provide?

It clarifies ion dynamics in nanoporous electrodes and supports interpretation of non-ideal cyclic voltammetry through a circuit-level representation tied to physics-based equations.

Aug 5, 2026

Upload by Oliver