Minimizing residuals of monotone discretizations yields the unique discrete solution to Hamilton-Jacobi equations together with explicit a posteriori error estimates and convergence to the viscosity solution.
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A certified adaptive quadrature framework computes guaranteed L^p, W^{1,p}, and W^{2,p} norms of deep neural networks by propagating interval enclosures on axis-aligned boxes.
Asymptotic-preserving neural networks infer viscoelastic parameters and reconstruct blood vessel state evolution from accessible ultrasound data in multiscale arterial flow models.
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.
citing papers explorer
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Solving Hamilton-Jacobi equations by minimizing residuals of monotone discretizations
Minimizing residuals of monotone discretizations yields the unique discrete solution to Hamilton-Jacobi equations together with explicit a posteriori error estimates and convergence to the viscosity solution.
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Certified and accurate computation of function space norms of deep neural networks
A certified adaptive quadrature framework computes guaranteed L^p, W^{1,p}, and W^{2,p} norms of deep neural networks by propagating interval enclosures on axis-aligned boxes.
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Asymptotic-Preserving Neural Networks for Viscoelastic Parameter Identification in Multiscale Blood Flow Modeling
Asymptotic-preserving neural networks infer viscoelastic parameters and reconstruct blood vessel state evolution from accessible ultrasound data in multiscale arterial flow models.
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A Mathematical Explanation of Transformers
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.