Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics (2212.07892v3)

Abstract: Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random variables rather than continuous measurements, or may be composed of measurements from multiple data modalities observed simultaneously. For instance, in neuroscience we may have behavioral labels in addition to spike counts and continuous physiological recordings. While by now there is a burgeoning literature on deep learning for dynamical systems reconstruction (DSR), multimodal data integration has hardly been considered in this context. Here we provide such an efficient and flexible algorithmic framework that rests on a multimodal variational autoencoder for generating a sparse teacher signal that guides training of a reconstruction model, exploiting recent advances in DSR training techniques. It enables to combine various sources of information for optimal reconstruction, even allows for reconstruction from symbolic data (class labels) alone, and connects different types of observations within a common latent dynamics space. In contrast to previous multimodal data integration techniques for scientific applications, our framework is fully \textit{generative}, producing, after training, trajectories with the same geometrical and temporal structure as those of the ground truth system.

• The paper introduces a novel multimodal generative framework using dendPLRNN and MVAEs for precise reconstruction of nonlinear dynamical systems.
• It integrates continuous and discrete data effectively, outperforming traditional methods like backpropagation through time in chaotic benchmarks.
• The approach enhances reconstruction accuracy under noisy conditions, paving the way for advanced applications in neuroscience, biology, and climate science.

An Examination of Multimodal Data Integration for Joint Generative Modeling of Complex Dynamics

The paper "Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics" presents a comprehensive framework designed to address the integration of multimodal data in the context of nonlinear dynamical systems reconstruction (DSR). Nonlinear dynamical systems often describe phenomena across various scientific fields, including neuroscience, biology, and climate science. Traditionally, these systems are explored through time series data. However, the complexity arises when such data is multimodal, consisting of both continuous and discrete observations, which is frequently the case in real-world applications. This paper advances an algorithmic solution leveraging multimodal variational autoencoders (MVAEs) for DSR tasks, proposing a novel framework that achieves better integration and inference of a system's dynamics from diverse data sources.

Framework Overview

At the core of the proposed framework is the dendritic piecewise linear recurrent neural network (dendPLRNN), which serves as the model for the generative reconstruction of nonlinear dynamical systems. The dendPLRNN is chosen for its mathematical tractability, allowing for analytical inquiries typically required in scientific settings. Coupled with this model is a set of modality-specific observation models, which allows the reconstruction algorithm to accommodate the distinct statistical properties of various data types, ranging from Gaussian, ordinal, and count data.

A significant innovation in this research is the use of MVAEs to generate a sparse teacher forcing signal, facilitating the training of the reconstruction model. This approach does not just integrate multiple modalities into a single latent representation but also ensures that diverse data sources contribute optimally to the reconstruction process. The employment of specialized training techniques such as sparse and generalized teacher forcing (STF and GTF) profoundly impacts the ability to reconstruct chaotic systems successfully — a notable achievement of the framework.

Numerical Results and Model Comparisons

The evaluation of the framework against other existing approaches, including sequential MVAEs and classical RNN training strategies such as backpropagation through time (BPTT), demonstrates superior performance. This superiority is evident across various benchmarks, including the notorious Lorenz and Rössler chaotic systems, where the proposed method exhibits lower state-space disagreement (D_{stsp}) and power spectrum Hellinger distance (D_H). Even in scenarios with high levels of noise or when only discrete data is available, the framework showcases its robustness by maintaining acceptable levels of reconstruction accuracy.

Implications and Future Directions

The implications of this research are substantial for fields reliant on accurately reconstructing and understanding complex system dynamics from limited or noisy data. The proposed framework enables the reconstruction of dynamical systems with a precision hitherto unattainable using prior methodologies, paving the way for deeper insights into complex temporal and geometrical system properties, which are invaluable in areas such as neuroscience and climate change modeling.

Moreover, the results challenge previous assumptions about the limitations of discrete data in capturing the intricate details of a system's dynamics. The successful reconstruction of chaotic attractors from purely symbolic representations suggests that future research could focus on optimizing algorithms to leverage such coarse-grained data further. This opens avenues for advancing theoretical understanding of how discrete or reduced representations relate to the continuous state spaces they approximate.

Overall, this work contributes significantly to the field of scientific machine learning by offering a model-agnostic, adaptable framework that efficiently reconciles the disparate demands of multimodal data integration and dynamical systems reconstruction. Future exploration might extend towards refining encoder-decoder architectures for greater scalability and exploring potential in real-time adaptive systems.