Scattering-based structural inversion of soft materials via Kolmogorov-Arnold networks

Chi Huan Tung; Lijie Ding; Ming Ching Chang; Guan Rong Huang; Lionel Porcar; Yangyang Wang; Jan Michael Y. Carrillo; Bobby G. Sumpter; Yuya Shinohara; Changwoo Do; Wei Ren Chen

doi:10.1063/5.0253877

Scattering-based structural inversion of soft materials via Kolmogorov-Arnold networks

Chi Huan Tung
, Lijie Ding
, Ming Ching Chang
, Guan Rong Huang
, Lionel Porcar
, Yangyang Wang
, Jan Michael Y. Carrillo
, Bobby G. Sumpter
, Yuya Shinohara
, Changwoo Do
, Wei Ren Chen

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov-Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.

Original language	English
Article number	074106
Journal	Journal of Chemical Physics
Volume	162
Issue number	7
DOIs	https://doi.org/10.1063/5.0253877
State	Published - Feb 21 2025

Funding

We sincerely acknowledge the insightful communications from Marco Heinen and Gerhard Nägele, whose valuable updates on the latest developments in the integral equation approach and its potential connections to data-driven machine learning methods have greatly enriched our understanding. This research was performed at the Spallation Neutron Source and the Center for Nanophase Materials Sciences, which are DOE Office of Science User Facilities operated by Oak Ridge National Laboratory. This research was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy and the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences, Data, Artificial Intelligence and Machine Learning at DOE Scientific User Facilities Program under Award No. 34532. The simulations and computations used resources of the Oak Ridge Leadership Computing Facility, which is supported by the DOE Office of Science under Contract No. DE-AC05-00OR22725. Y.S. was supported by the U.S. DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. G.R.H. received support from the National Science and Technology Council (NSTC) in Taiwan under Grant No. NSTC 111-2112-M-110-021-MY3. We acknowledge the allocation of beam time on the D22 small-angle neutron scattering diffractometer at the Institut Laue-Langevin (ILL), which was instrumental to the success of this research. We thank ILL for the provision of beam time on the D22 SANS instrument DOI: 10.5291/ILL-DATA.EASY-1421 .

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10.1063/5.0253877

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title = "Scattering-based structural inversion of soft materials via Kolmogorov-Arnold networks",

abstract = "Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov-Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.",

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AU - Tung, Chi Huan

AU - Ding, Lijie

AU - Chang, Ming Ching

AU - Huang, Guan Rong

AU - Porcar, Lionel

AU - Wang, Yangyang

AU - Carrillo, Jan Michael Y.

AU - Sumpter, Bobby G.

AU - Shinohara, Yuya

AU - Do, Changwoo

AU - Chen, Wei Ren

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Y1 - 2025/2/21

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AB - Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov-Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.

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Scattering-based structural inversion of soft materials via Kolmogorov-Arnold networks

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