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This paper integrates modern Hopfield networks with a port-Hamiltonian neural ODE, enabling by design the construction of barrier functions yielding explicit admissible-input sets and quantitative robustness radii that are more robust to external solicitations than comparable existing approaches.
It is shown that the state distribution of the system can be tractably approximated over time by Gaussian mixture distributions, with formal error bounds in Wasserstein distance, which yields closed-form expressions for expected costs and chance constraints.
Clustered $\alpha$-smoothing is proposed, a framework that partitions noisy samples using an arbitrary clustering algorithm, applies $\alpha$-smoothing locally within each cluster, and combines the resulting predictions into a mixture distribution, derived from interpreting the smoothing distribution as a mixture of $\...
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