ML: Dynamics

Machine-learning ideas tagged Dynamics in the ML taxonomy of the Math2NN corpus.

Unverified 2026

Hard Sequential Neural ODE Solver

Partition a long integration interval into M short segments and assign one neural trajectory approximator to each segment. Instead of asking a single network to satisfy the ODE and initial condition over the entire horizon, construct every segment so that its value at the left boundary is exactly the terminal value predicted by the previous segment. This removes interface discontinuities from the optimization problem and should improve long-horizon trajectory accuracy and gradient stability.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Modeling of an ODE-constrained optimization problem describing tumor dynamics, and numerical approximation via sequential physics-informed neural networks arXiv:2608.18974