Nonlinear Dynamical Modeling of Human Intracranial Brain Activity with Flexible Inference

TL;DR

The paper tackles forecasting multisite human iEEG dynamics by augmenting a linear latent dynamical backbone with nonlinear manifold embeddings (DFINE). By training end-to-end and employing Kalman-filter-based flexible inference, DFINE captures nonlinear structure while remaining robust to missing observations. Across 10 subjects, DFINE outperforms a linear state-space model and matches or surpasses a GRU baseline, with the largest gains in high gamma power and when data dropout occurs. These results establish a scalable, interpretable framework for modeling human iEEG dynamics with potential applications in next-generation brain–computer interfaces and clinical neuroengineering.

Abstract

Dynamical modeling of multisite human intracranial neural recordings is essential for developing neurotechnologies such as brain-computer interfaces (BCIs). Linear dynamical models are widely used for this purpose due to their interpretability and their suitability for BCIs. In particular, these models enable flexible real-time inference, even in the presence of missing neural samples, which often occur in wireless BCIs. However, neural activity can exhibit nonlinear structure that is not captured by linear models. Furthermore, while recurrent neural network models can capture nonlinearity, their inference does not directly address handling missing observations. To address this gap, recent work introduced DFINE, a deep learning framework that integrates neural networks with linear state-space models to capture nonlinearities while enabling flexible inference. However, DFINE was developed for intracortical recordings that measure localized neuronal populations. Here we extend DFINE to modeling of multisite human intracranial electroencephalography (iEEG) recordings. We find that DFINE significantly outperforms linear state-space models (LSSMs) in forecasting future neural activity. Furthermore, DFINE matches or exceeds the accuracy of a gated recurrent unit (GRU) model in neural forecasting, indicating that a linear dynamical backbone, when paired and jointly trained with nonlinear neural networks, can effectively describe the dynamics of iEEG signals while also enabling flexible inference. Additionally, DFINE handles missing observations more robustly than the baselines, demonstrating its flexible inference and utility for BCIs. Finally, DFINE's advantage over LSSM is more pronounced in high gamma spectral bands. Taken together, these findings highlight DFINE as a strong and flexible framework for modeling human iEEG dynamics, with potential applications in next-generation BCIs.

Figures (10)

• Figure 1: Model architecture of DFINE. (a) The generative model of DFINE is shown. DFINE uses two sets of latent factors: the dynamic and manifold latent factors. The dashed connection from neural observations to the manifold latent factor is used only during inference. (b) The inference procedure with DFINE is shown. We first estimate the manifold latent factors using the nonlinear manifold embedding at each timestep. Using the dynamic equation, we recursively run the Kalman filter to infer the dynamic latent factor $x_{t|t}$ and predict the next dynamic latent factor by using the Kalman predictor to obtain first $x_{t+1|t}$ and then $a_{t+1|t}$. Finally, to predict the observation in the future, DFINE maps Kalman predicted manifold factor through the decoder to estimate $\hat{y}_{t+1|t}$. All model parameters (LDM and autoencoder) are trained jointly to learn the best nonlinear embeddings over which the dynamics can be linear.
• Figure 2: Experimental methodologies. (a) $N$-fold cross-validation of the continuous iEEG activity. The gray gaps are excluded to avoid information leakage across train, valid, and test sets. (b) The model fitting and evaluation procedure for each of the $N$ folds.
• Figure 3: Across the population and within each subject, DFINE (green) outperforms LSSM (yellow) and the naive predictor (pink) on one-step-ahead neural prediction, while performing on par with (matching or exceeding) GRU (blue). Asterisks show significance (*: $p<0.05$, **: $p<0.01$, ***: $p<0.001$, and n.s.: $p>0.05$; one-sided and two-sided Wilcoxon with LSSM and GRU, respectively). Whiskers indicate s.e.m. and each dot represents the test performance for one held-out fold.
• Figure 4: Three iEEG power features and their corresponding prediction traces by DFINE (green) and LSSM (yellow) in a single subject. DFINE clearly better predicts the future iEEG activity better than LSSM.
• Figure 5: DFINE maintains superior multi-step-ahead prediction accuracy, outperforming all baselines. Solid curves represent the mean and the shaded regions denote the standard error of the mean (SEM) of all test folds pooled across the 10 subjects. Asterisks indicate significance (***:$p<0.001$, blue, yellow, and red indicating comparisons against GRU, LSSM, and naive, respectively).