Encounter and Merging of Mesh-based Methods and Meshless Methods in the Era of Machine Learning
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Shuo Zhang
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Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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Peoples Rep of China
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Haijun Yu
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Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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Peoples Rep of China
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Chensong Zhang
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Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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Peoples Rep of China
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Introduction:
| | Computational science and engineering depend on numerical methods to solve complex PDEs and model real-world systems. Two dominant paradigms -- mesh-based methods (e.g., FEM, FDM, FVM) and meshless methods (e.g., RBF, MLS, MG) -- have long coexisted but faced complementary limitations. Mesh-based methods, while mathematically rigorous and tool-mature, struggle with high computational costs for complex geometries, adaptive refinement, and high-dimensional problems. Meshless methods, though geometrically flexible, suffer from dense matrix operations, weak error bounds, and poor scalability. Meanwhile, machine learning (ML) -- with its strengths in pattern learning, high-dimensional optimization, and surrogate modeling -- has revolutionized scientific computing. This symposium explores the convergence of these three fields, aiming to transcend traditional limitations and unlock hybrid frameworks that are robust, scalable, and versatile.
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