Latent Diffeomorphic Dynamic Mode Decomposition
This work addresses the challenge of modeling complex non-linear systems with memory for applications like streamflow prediction, representing an incremental improvement by hybridizing existing methods.
The paper tackled the problem of analyzing non-linear systems by introducing Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), which combines the interpretability of Dynamic Mode Decomposition with the predictive power of Recurrent Neural Networks, resulting in accurate predictions as demonstrated in streamflow prediction.
We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of Recurrent Neural Networks (RNNs). Notably, LDDMD maintains simplicity, which enhances interpretability, while effectively modeling and learning complex non-linear systems with memory, enabling accurate predictions. This is exemplified by its successful application in streamflow prediction.