# Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition

arXiv: https://arxiv.org/abs/1409.5496 · HTML: https://mlsanity.com/paper/1409.5496/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2014.

## Built on by (most cited first, 30 of 49)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
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- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Residual Dynamic Mode Decomposition: Robust and verified Koopmanism](https://mlsanity.com/paper/2205.09779/) (2022)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Koopman neural operator as a mesh-free solver of non-linear partial differential equations](https://mlsanity.com/paper/2301.10022/) (2023)
- [Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis](https://mlsanity.com/paper/2306.10168/) (2023)
- [The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems](https://mlsanity.com/paper/2209.02244/) (2022)
- [Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems](https://mlsanity.com/paper/2308.10697/) (2023)
- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Adversarial dynamical systems characterize when data-driven learning succeeds or fails](https://mlsanity.com/paper/2407.06312/) (2024)
- [KoopmanLab: machine learning for solving complex physics equations](https://mlsanity.com/paper/2301.01104/) (2023)
- [Identifying Equivalent Training Dynamics](https://mlsanity.com/paper/2302.09160/) (2023)
- [Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2403.02524/) (2024)
- [Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics](https://mlsanity.com/paper/2405.11955/) (2024)
- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties](https://mlsanity.com/paper/2106.06033/) (2021)
- [KODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operators](https://mlsanity.com/paper/2409.19518/) (2024)
- [Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds](https://mlsanity.com/paper/2603.15091/) (2026)
- [Analysis, forecasting and system identification of a floating offshore wind turbine using dynamic mode decomposition](https://mlsanity.com/paper/2411.07263/) (2024)
- [Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling](https://mlsanity.com/paper/2504.13333/) (2025)
- [Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor](https://mlsanity.com/paper/2510.12368/) (2025)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [On the Convergence of Hermitian Dynamic Mode Decomposition](https://mlsanity.com/paper/2401.03192/) (2024)
- [RePST: Language Model Empowered Spatio-Temporal Forecasting via Semantic-Oriented Reprogramming](https://mlsanity.com/paper/2408.14505/) (2024)
- [Model-free system identification of surface ships in waves via Hankel dynamic mode decomposition with control](https://mlsanity.com/paper/2502.15782/) (2025)
- [Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections](https://mlsanity.com/paper/2102.09973/) (2021)
- [A parametric framework for kernel-based dynamic mode decomposition using deep learning](https://mlsanity.com/paper/2409.16817/) (2024)

## Abstract (arXiv)

There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to hours. Such dynamic datasets are characterized by coherent patterns across both space and time, yet existing computational methods are typically restricted to analysis either in space or in time separately. Here we report the adaptation of dynamic mode decomposition (DMD), an algorithm originally developed for the study of fluid physics, to large-scale neuronal recordings. DMD is a modal decomposition algorithm that describes high-dimensional dynamic data using coupled spatial-temporal modes; the resulting analysis combines key features of performing principal components analysis (PCA) in space and power spectral analysis in time. The algorithm scales easily to very large numbers of simultaneously acquired measurements. We validated the DMD approach on sub-dural electrode array recordings from human subjects performing a known motor activation task. Next, we leveraged DMD in combination with machine learning to develop a novel method to extract sleep spindle networks from the same subjects. We suggest that DMD is generally applicable as a powerful method in the analysis and understanding of large-scale recordings of neural activity.