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We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in $\mathbb{R}^d$, where $d\ge 1$.
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The heterogeneous multi-scale methods
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A multiscale discontinuous galerkin method with the computational structure of a continuous galerkin method
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Frei Mark G and Osorio Ivan · 2007
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Heterogeneous multiscale methods: a review
E Weinan, Bjorn Engquist, Xiantao Li, Weiqing Ren, and Eric Vanden-Eijnden · 2007
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Grigoris Pavliotis and Andrew Stuart · 2008
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H-convergence
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Reinforced dynamics for enhanced sampling in large atomic and molecular systems
Linfeng Zhang, Han Wang, and Weinan E · 2018
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Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
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A bayesian numerical homogenization method for elliptic multiscale inverse problems
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Stochasticity of deterministic gradient descent: Large learning rate for multiscale objective function
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Drift estimation of multiscale diffusions based on filtered data
Assyr Abdulle, Giacomo Garegnani, Grigorios A Pavliotis, Andrew M Stuart, and Andrea Zanoni · 2021
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Mixed finite element approximation of periodic hamilton–jacobi–bellman problems with application to numerical homogenization
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Multiscale modeling meets machine learning: What can we learn?
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Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions
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Asymptotic-preserving schemes for multiscale physical problems
Shi Jin · 2022
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Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations
Shi Jin, Zheng Ma, and Keke Wu · 2023
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