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arXiv · 2609.23930

AI-assisted analytical theory in soft matter and multiphysics: new results and lessons from diffusiophoresis and bipolar membranes

Ankur Gupta
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Abstract

We present a framework to advance analytical theory in the area of soft matter and multiphysics using assistance from AI. The framework emphasizes (i) setting "honesty rules", (ii) focusing on a few key papers that are used to formulate a problem of interest, (iii) specifying checks a priori, (iv) using only one task per session and keeping a running log of tasks, checks, corrections, and sessions so that a mistake is not propagated through a project, and (v) ensuring all decisions are approved by humans while AI focuses primarily on execution. The framework is applied to two distinct problems to create new knowledge, including (i) diffusiophoresis of a spherical particle in the presence of an arbitrary number of electrolytes at arbitrary Debye lengths, and (ii) analytical description of I-V curves, including overlimiting current, in bipolar membranes without including the water dissociation kinetics. Both of these problems are advanced analyses and would each typically require several months to a year's worth of effort, but were solved in a matter of a few days. However, the increased efficiency should be cautiously navigated to avoid cognitive offloading and ensure that AI-assisted results are used to extract human-readable insights instead of just reporting a new mathematical formula. The usage of AI is transparently presented. Finally, we also share brief thoughts on how to integrate AI tools in theoretical research during graduate education.

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Ankur Gupta. 2026-09-20. AI-assisted analytical theory in soft matter and multiphysics: new results and lessons from diffusiophoresis and bipolar membranes. https://arxiv.org/abs/2609.23930

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