Projected EDMD-DL is structurally a neural ODE: it lifts the state through a learned dictionary, evolves or differentiates with a linear map, and projects back; on Lorenz and a nine-mode shear flow it performs comparably to directly trained neural ODEs.
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On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictions
Projected EDMD-DL is structurally a neural ODE: it lifts the state through a learned dictionary, evolves or differentiates with a linear map, and projects back; on Lorenz and a nine-mode shear flow it performs comparably to directly trained neural ODEs.