Out-of-Domain Generalization in Dynamical Systems Reconstruction for Neurophysiological Time Series

• Applicant: Professor Dr. Daniel Durstewitz
• Subject Area: Experimental and Theoretical Network Neuroscience
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567025973

In dynamical systems reconstruction (DSR), we aim to infer from time series measurements a generative dynamical systems (DS) model of the dynamical process, i.e. the governing equations, underlying the empirically observed data. A successfully reconstructed DS should agree in important topological and geometrical characteristics (e.g. of attractor states) with the true (but unknown) underlying DS, as well as with its (long-term) temporal behavior. DSR is currently a burgeoning field in machine learning (ML) and AI, to which our group has substantially contributed over the past couple of years. DSR techniques, often based on deep recurrent neural networks (RNNs), offer great potential in theoretical neuroscience as scientific discovery tools: They enable to infer from neurophysiological and behavioral recordings dynamically accurate computational models that can be further analyzed, probed, perturbed, and simulated. A big open question in DSR, as in ML/AI more generally currently, however, is that of out-of-domain (OOD) generalization: Can a successfully trained DSR model predict the dynamics in other regions of state space (possibly in different attractor basins), or under different parameter configurations, than those experienced during model training? For instance, can a DSR model trained only on ‘normal’ physiological activity successfully predict transitions into epileptic activity under parameter variations, or can it quantitatively predict the impact of optogenetic manipulations on neural dynamics? If trained on neural and behavioral recordings from only one set of behavioral rules, can it predict physiological activity and behavior on a novel set of rules not seen in training? Progress along these lines could have tremendous impact on neuroscience research, and beyond, in other areas where formal models of empirical phenomena are sought. Here we are going to address this question through mathematical analysis, numerical experiments, the design of novel ML model architectures and algorithms, and on neurophysiological and behavioral datasets. In work package (WP) 1, we will study recently advanced, and design novel, architectures for DSR foundation models which show promise for extracting from diverse training data generalizable principles and could tackle specific weaknesses in current DSR algorithms we have identified recently. In WP 2 we will focus on strategies for enabling OOD generalization via integration of biological priors in the form of a) known biophysical equation models and b) synaptic connectivity information into the model inference. All DSR model algorithms will be evaluated on a set of carefully chosen benchmark systems. In WP 3 we will test the most promising algorithms for OOD generalization on neurophysiological and behavioral data, testing generalization to behavioral rules and neural activity not provided for model training, and generating novel predictions for further behavioral and optogenetic experiments.

• DFG Programme: Research Grants