Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties
Not Available
Mallen, Alex T. (ORCID:0000000251201350)↗
Engineering topics
Kutz, J. Nathan
Publications and source records attributed to Kutz, J. Nathan.
Attention for Causal Relationship Discovery from Biological Neural Dynamics
This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks. Our study primarily focuses on a proof-of-concept investigation based on simulated neural dynamics, for which the ground-truth causality is known through the underlying connectivity matrix. For transformer models trained to forecast neuronal population dynamics, we show that the cross-attention module effectively captures the causal relationship among neurons, with an accuracy equal to or superior to that of the most popular Granger causality discovery method. While we acknowledge that real-world neurobiology data will bring further challenges, including dynamic connectivity and unobserved variability, this research offers an encouraging preliminary glimpse into the utility of the transformer model for causal representation learning in neuroscience.
Lu, Ziyu↗
Multiresolution convolutional autoencoders
Herein we propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.
97 MATHEMATICS AND COMPUTING↗