Runge-Kutta Solvers
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Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers
Announce Type: replace Abstract: Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit exact inversion, an inaccuracy that is unacceptable in precision-critical...
amerta: A Python Library for Idealized 1D Saint--Venant Dam-Break Simulation
arXiv:2605.31011v1 Announce Type: new Abstract: The Saint-Venant shallow water equations (SWE) govern depth-integrated free-surface flows arising in dam-break inundation, flood routing, tsunami runup, and estuarine tidal dynamics. Closed-form analytical solutions exist only for highly idealized Riemann configurations, making rigorously verified numerical solvers essential. This work presents amerta, an open-source Python library that solves the one-dimensional frictionless Saint-Venant...