Proves O((α_n n)^{-1/2}) convergence of GNDE trajectories and adjoints to Graphon-NDE limits on sparse random graphs, with DTO/OTD consistency and experimental support for zero-shot transfer.
A stable and scalable method for solving initial value PDEs with neural networks
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cs.LG 2years
2026 2representative citing papers
A new Dirac-Frenkel-Onsager dynamics injects gauge momentum to achieve unbiased, temporally smooth parameter evolution for nonlinear PDE approximations.
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Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence
Proves O((α_n n)^{-1/2}) convergence of GNDE trajectories and adjoints to Graphon-NDE limits on sparse random graphs, with DTO/OTD consistency and experimental support for zero-shot transfer.
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A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions
A new Dirac-Frenkel-Onsager dynamics injects gauge momentum to achieve unbiased, temporally smooth parameter evolution for nonlinear PDE approximations.