Numerical methods for evolutionary differential equations

By Ernst Hairer. 2010

108 citations recorded by the source corpus.

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1. Jens Behrmann
2. David Kristjanson Duvenaud
3. Lars Ruthotto
4. Jörn-Henrik Jacobsen
5. Eldad Haber
6. Samy Wu Fung
7. Lili Meng
8. Bo-Hao Chang

Citations in the corpus

• Invertible Residual Networks (2018, background): “Contrarily, initial value problems on [0 , T ] are well-posed for Lipschitz continuous dynamics [4].”
• OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport (2020, methodology): “, when the neural network parameters lead to a stiff ODE or dynamics that change quickly in time [3].”
• Stable architectures for deep neural networks (2017, methodology): “The Hamiltonian networks require special integration techniques; see [2] for details on their treatment.”
• Reversible Architectures for Arbitrarily Deep Residual Neural Networks (2017, methodology): “Such problems have rich theoretical and computational framework, including techniques to guarantee stable networks by using appropriate functions F , the discretization of the forward propagation process (Ascher and Petzold 1998; Ascher 2010; Bellman 1953), theoretical frameworks for the optimizatio”