Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

The paper clearly specifies the EDMD-DL objective, alternating closed-form K update, and NODE-based dictionary with adjoint training, and reports concrete Duffing and Kuramoto–Sivashinsky results and parameter counts (Tables 1–5) under stated data-generation and solver settings, e.g., DOPRI5(4) with abs/rel tolerances 1e−9/1e−7, M=25 for Duffing with 3 non-trainable outputs, and M=151 with 129 non-trainable for KS. These are internally consistent and sufficient for replication (loss and K-update: Eqs. (20)–(21); metrics: Eqs. (28)–(32); architecture/adjoint: Eq. (25)–(27); prediction: Eq. (19)) . By contrast, the candidate solution only proposes a plan and does not execute or report the quantitative metrics. It also deviates by fixing the output projection (the paper states the input and output layers are the same as in the MLP-based EDMD-DL) which affects parameter counting and comparability . Given the paper’s explicit numerical evidence (Duffing Tables 1–2, classification Table 3; KS Tables 4–5), the paper’s claims stand, while the model solution is incomplete and not validated .