# A scalable generative model for dynamical system reconstruction from neuroimaging data arXiv: https://arxiv.org/abs/2411.02949 ยท HTML: https://mlsanity.com/paper/2411.02949/ ## Key facts - Cited by 9 papers in the map (data through 14 Oct 2026). - Builds on 23 of its 82 references that are in the map. - First posted on arXiv 5 Nov 2024. ## Builds on (most cited first, 23 of 23) - [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018) - [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018) - [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019) - [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020) - [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021) - [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023) - [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023) - [Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI](https://mlsanity.com/paper/1902.07186/) (2019) - [Lyapunov spectra of chaotic recurrent neural networks](https://mlsanity.com/paper/2006.02427/) (2020) - [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022) - [Recurrent switching linear dynamical systems](https://mlsanity.com/paper/1610.08466/) (2016) - [On Lyapunov Exponents for RNNs: Understanding Information Propagation Using Dynamical Systems Tools](https://mlsanity.com/paper/2006.14123/) (2020) - [A State Space Approach for Piecewise-Linear Recurrent Neural Networks for Reconstructing Nonlinear Dynamics from Neural Measurements](https://mlsanity.com/paper/1612.07846/) (2016) - [DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization](https://mlsanity.com/paper/2108.00069/) (2021) - [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021) - [Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systems](https://mlsanity.com/paper/2301.10321/) (2023) - [Homotopy-based training of NeuralODEs for accurate dynamics discovery](https://mlsanity.com/paper/2210.01407/) (2022) - [Learn to Synchronize, Synchronize to Learn](https://mlsanity.com/paper/2010.02860/) (2020) - [Deep-OSG: Deep Learning of Operators in Semigroup](https://mlsanity.com/paper/2302.03358/) (2023) - [lfads-torch: A modular and extensible implementation of latent factor analysis via dynamical systems](https://mlsanity.com/paper/2309.01230/) (2023) - [Gradient Flossing: Improving Gradient Descent through Dynamic Control of Jacobians](https://mlsanity.com/paper/2312.17306/) (2023) - [Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation](https://mlsanity.com/paper/1611.07999/) (2016) - [Biophysically grounded mean-field models of neural populations under electrical stimulation](https://mlsanity.com/paper/1906.00676/) (2019) ## Built on by (most cited first, 9 of 9) - [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025) - [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026) - [MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems](https://mlsanity.com/paper/2604.06881/) (2026) - [Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data](https://mlsanity.com/paper/2509.00924/) (2025) - [Scalable Diffusion Transformer for Conditional 4D fMRI Synthesis](https://mlsanity.com/paper/2511.22870/) (2025) - [Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems](https://mlsanity.com/paper/2504.09750/) (2025) - [Autoregressive One-Step Generative Modeling for Dynamical System Forecasting](https://mlsanity.com/paper/2605.05540/) (2026) - [Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction](https://mlsanity.com/paper/2605.12683/) (2026) - [Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics](https://mlsanity.com/paper/2608.16569/) (2026) ## Abstract (arXiv) Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models based on biophysical principles and allow to automatize the inference of inter-individual differences in brain dynamics. Recent breakthroughs in training techniques for state space models (SSMs) specifically geared toward dynamical systems (DS) reconstruction (DSR) enable to recover the underlying system including its geometrical (attractor) and long-term statistical invariants from even short time series. These techniques are based on control-theoretic ideas, like modern variants of teacher forcing (TF), to ensure stable loss gradient propagation while training. However, as it currently stands, these techniques are not directly applicable to data modalities where current observations depend on an entire history of previous states due to a signal's filtering properties, as common in neuroscience (and physiology more generally). Prominent examples are the blood oxygenation level dependent (BOLD) signal in functional magnetic resonance imaging (fMRI) or Ca2+ imaging data. Such types of signals render the SSM's decoder model non-invertible, a requirement for previous TF-based methods. Here, exploiting the recent success of control techniques for training SSMs, we propose a novel algorithm that solves this problem and scales exceptionally well with model dimensionality and filter length. We demonstrate its efficiency in reconstructing dynamical systems, including their state space geometry and long-term temporal properties, from just short BOLD time series.