Neural ODEs

Neural ODEs represent hidden states or physical systems as evolving continuously according to a learned vector field, with numerical solvers used to compute their trajectories. Researchers use them for irregular time-series forecasting, scientific simulation, control, and generative modeling, often combining them with controlled or stochastic dynamics, graph networks, or known physical laws. Common approaches include hybrid mechanistic-neural models, physics-informed constraints, and structure-preserving methods such as Hamiltonian or symplectic models; evaluations span dynamical-system benchmarks, irregular clinical data, and engineering simulations. A central tension is balancing flexible learned dynamics with physical consistency and long-horizon reliability, while managing solver cost, stiffness, noisy observations, and sensitivity to numerical error.