Data-Driven Modeling of Dynamical Systems

In this this project, we perform a comparative evaluation of Extended Dynamic Mode Decomposition (EDMD) and Neural Ordinary Differential Equations (Neural ODEs) for trajectory modeling in both linearly immersible and chaotic dynamical systems.Data-driven operator inference lifts snapshot data into a feature space—via explicit dictionary functions or the kernel trick—and computes a finite-dimensional approximation of the Koopman operator through truncated SVD. In parallel, Neural ODEs parameterize the continuous-time vector field with a neural network, trained end-to-end using forward- and adjoint-sensitivity methods.

We quantify model fidelity by the root-mean-square error (RMSE) over multiple simulated trajectories of the Lotka–Volterra predator–prey and Lorenz systems. This study illuminates the trade-off between EDMD’s robustness, interpretability, and low computational cost versus Neural ODE’s expressiveness, adaptivity, and ability to capture highly nonlinear transients. For a more detailed summary of the results please refer to the project slides.