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Stability-Informed Initialization of Neural Ordinary Differential Equations
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This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver's corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.
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Learning to Integrate
A transport map learned by normalizing flows turns Smolyak sparse Gauss-Hermite quadrature nodes into nodes for a non-Gaussian distribution, enabling expectation estimates for PDE outputs with far fewer simulation runs.
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