Deep state-space models (DSSMs) are rich frameworks for modeling complex temporal dynamics in sequential data. They provide interpretable representations of the physical processes, account for latent factors, and leverage DNN capacity to capture nonlinear dependencies in high-dimensional settings. The thesis will develop DSSMs that continuously learn from and adapt to different data regimes using continual learning strategies. The student will explore the definition of distribution shift and investigate intervention strategies that can be distinguished from natural drift in the data using GANs, Autoencoders, or Knockoffs. Further on, CD methods are developed on the subsystems level using higher-order information decomposition. A central focus will be identifying interpretable low-dimensional features for each subsystem that remain predictable across multiple environments and/or scales. These features help define optimal representations of system states, improving CD generalization and allowing for multiscale CD. Finally, data augmentation techniques using PINN or symbolic regression will be developed to mitigate bias in training data. The developed causal models are validated on the CausalRivers benchmark using subsampled datasets simulating non-stationary, high-dimensional, and distribution shift settings.
