Introduction to PySHRED

What is PySHRED?

PySHRED is a Python package implementing the SHallow REcurrent Decoder (SHRED) architecture for sensing applications. PySHRED achieves state-of-the-art accuracy on full-state reconstructions and forecasting of spatiotemporal dynamics from very few sensors.

The three core components of PySHRED are the sequence, decoder, and latent forecaster models.

• Sequence model: a neural architecture that learns the temporal dependencies in sensor measurements and projects them into a low-dimensional latent representation.

• Decoder model: a neural architecture that learns a mapping between the low-dimensional latent representation and the high-dimensional state space.

• Latent forecaster model: a model that takes in the current latent states and predicts the future latent states.

The sequence and decoder models work together to reconstruct the high-dimensional state space from sensor measurements. The latent forecaster and decoder models work together to forecast high-dimensional state space dynamics without needing additional sensor measurements.

PySHRED achieves amazing performance on most applications straight out-of-the-box. If you want to build your own SHRED model optimized for your application, PySHRED allows you to seamlessly mix-and-match different built-in sequence, decoder, and latent forecaster models. Furthermore, you can customize the architecture of each specific sequence/decoder/latent forecaster model to best fit your specific application.

Figure: The SHRED architecture includes a sequence model that encodes temporal sensor dynamics into a low-dimensional latent space, and a decoder that reconstructs the full-state space from that latent representation. Additionally, SHRED includes a latent forecaster model to predict the future evolution of the latent space, which is decoded to reconstruct the future full-state spatiotemporal dynamics.

When to use PySHRED?

PySHRED is a powerful tool for any application involving the reconstruction/forecasting of spatiotemporal dynamics from timeseries sensors measurements.

• Reconstruction is a sensing task involving the inference of full-state system dynamics from sensor measurements.

• Forecasting is a sensing task involving the inference of future full-state system dynamics without using additional sensor measurements.

Note: PySHRED is a supervised learning model, and requires access to full-state data during training.

Related Publications

PySHRED is built on cutting-edge research at the nexus of machine learning and dynamical systems. To learn more about the underlying research, methodology, and real-world applications, refer to the following publications:

• Williams, J. P., Zahn, O., & Kutz, J. N. (2024).
  Sensing with shallow recurrent decoder networks.
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2298), 20240054.

• Gao, M. L., Williams, J. P., & Kutz, J. N. (2025).
  Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks.
  arXiv preprint, arXiv:2501.13329.

• Tomasetto, M., Williams, J. P., Braghin, F., Manzoni, A., & Kutz, J. N. (2025).
  Reduced Order Modeling with Shallow Recurrent Decoder Networks.
  arXiv preprint, arXiv:2502.10930.

• Kutz, J. N., Reza, M., Faraji, F., & Knoll, A. (2024).
  Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics.
  arXiv preprint, arXiv:2405.11955.

• Ebers, M. R., Williams, J. P., Steele, K. M., & Kutz, J. N. (2024).
  Leveraging arbitrary mobile sensor trajectories with Shallow Recurrent Decoder Networks for full-state reconstruction.
  IEEE Access, 12, 97428–97439.