Recent Developments in Gradient Flows: Theory, Numerics, and Applications
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Organizer(s): |
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Affiliation:
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Country:
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Chaoyu Quan
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The Chinese University of Hong Kong (Shenzhen)
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Peoples Rep of China
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Xiaoming Wang
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Eastern Institute of Technology
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Peoples Rep of China
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Jiang Yang
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Southern University of Science and Technology
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Peoples Rep of China
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Introduction:
| | Gradient flows play a fundamental role in modeling dissipative evolution in various scientific and engineering disciplines. Recent advancements have significantly enhanced the theoretical understanding, numerical analysis, and practical applications of these flows. This special session will focus on cutting-edge developments for gradient flows, including theoretical anlaysis, structure-preserving discretizations, variational approaches, and machine-learning-assisted solvers. Topics of interest include, but are not limited to, energy-stable schemes, adaptive algorithms, optimization techniques, and their applications in fluid dynamics, material sciences, and image processing. A particular emphasis will be placed on novel numerical frameworks that ensure stability, efficiency, and accuracy, addressing key challenges in high-dimensional and complex systems. By bringing together experts from diverse backgrounds, this session aims to foster discussions on emerging trends and future directions in computational methods for gradient flows. We welcome contributions from both theoretical and applied perspectives to advance the numerical treatment of these important mathematical models.
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