sindy-shred
SINDy-SHRED: Sparse Identification of Nonlinear Dynamics with SHallow REcurrent Decoder Networks
📌 Overview
SINDy-SHRED is a method for spatiotemporal modeling of real-world data that integrates sensing and model identification using a shallow recurrent decoder network. It efficiently reconstructs the full spatiotemporal field from a few sensor measurements while enforcing interpretable latent space dynamics.
- Sparse Identification of Nonlinear Dynamics (SINDy) regularization ensures latent space dynamics follow a SINDy-class functional.
- Gated Recurrent Units (GRUs) handle sequential sensor measurements.
- Shallow decoder network reconstructs the high-dimensional field from latent variables.
- Koopman-SHRED variant enforces linear latent space dynamics using Koopman theory.
- Minimal hyperparameter tuning required; runs efficiently on laptop-level computing.
SINDy-SHRED achieves state-of-the-art performance in various applications, including:
- ✅ Synthetic PDE data modeling
- ✅ Sea Surface Temperature (SST) prediction from real sensor data
- ✅ Long-term video forecasting
📝 Paper
📄 Title: Sparse Identification of Nonlinear Dynamics with SHallow REcurrent Decoder networks (SINDy-SHRED)
🔗 Preprint: arXiv:2501.13329
🔧 Installation
Dependencies
- Python 3.8+
- PyTorch
- NumPy
- SciPy
- Matplotlib
- scikit-learn
🚀 Quick Start in Google Colab
We strongly encourage you to explore SINDy-SHRED by directly running our Colab notebook. The colab notebook allows you to easily reproduce experiments, and understand the workflow without any setup:
✨ Just plug and play! 🎸
📂 Dataset
Please download the dataset and place it into the Data/ folder, as GitHub might mistakenly ignore large files.
Download Link: 🔗 Google Drive: Dataset
🚀 Usage
1️⃣ Define Train a SINDy-SHRED model
import sindy_shred
library_dim = sindy_shred.library_size(latent_dim, poly_order, include_sine, True)
# Initialize and train the SINDy-SHRED model
shred = sindy_shred.SINDy_SHRED(
num_sensors, m, hidden_size=3, hidden_layers=2, l1=350, l2=400, dropout=0.1,
library_dim=library_dim, poly_order=3, include_sine=False, dt=1/52.0*0.1, layer_norm=False
)
validation_errors = sindy_shred.fit(
shred, train_dataset, valid_dataset, batch_size=128, num_epochs=600, lr=1e-3, verbose=True,
threshold=0.25, patience=5, sindy_regularization=10.0, optimizer="Lion", thres_epoch=100
)
📊 Results & Benchmarks
SINDy-SHRED outperforms state-of-the-art models on real and synthetic datasets, including:
- ✅ Convolutional LSTM
- ✅ PredRNN
- ✅ ResNet
- ✅ SimVP
🌍 Real-World SST Data Example
💨 Flow over a Cylinder Example
🌪 Isotropic Turbulent Flow Example
📽 Pendulum Video Prediction Example
📉 Visualizing the Loss Landscape
📖 Citation
If you find SINDy-SHRED useful in your research, please cite:
@misc{gao2025sparse,
title={Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks},
author={Mars Liyao Gao and Jan P. Williams and J. Nathan Kutz},
year={2025},
eprint={2501.13329},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2501.13329},
}