Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans, where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called "eigenworms"). We find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create "interaction profiles" to represent an individual's behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.

An important approach for scientific inquiry across many disciplines involves using observational time series data to understand the relationships between key variables to gain mechanistic insights into the underlying rules that govern the given system. In real systems, such as those found in ecology, the relationships between time series variables are generally not static; instead, these relationships are dynamical and change in a nonlinear or state-dependent manner. To further understand such systems, we investigate integrating methods that appropriately characterize these dynamics (i.e., methods that measure interactions as they change with time-varying system states) with visualization techniques that can help analyze the behavior of the system. Here, we focus on empirical dynamic modeling (EDM) as a state-of-the-art method that specifically identifies causal variables and measures changing state-dependent relationships between time series variables. Instead of using approaches centered on parametric equations, EDM is an equation-free approach that studies systems based on their dynamic attractors. We propose a visual analytics system to support the identification and mechanistic interpretation of system states using an EDM-constructed dynamic graph. This work, as detailed in four analysis tasks and demonstrated with a GUI, provides a novel synthesis of EDM and visualization techniques such as brush-link visualization and visual summarization to interpret dynamic graphs representing ecosystem dynamics. We applied our proposed system to ecological simulation data and real data from a marine mesocosm study as two key use cases. Our case studies show that our visual analytics tools support the identification and interpretation of the system state by the user, and enable us to discover both confirmatory and new findings in ecosystem dynamics. Overall, we demonstrated that our system can facilitate an understanding of how systems function beyond the intuitive analysis of high-dimensional information based on specific domain knowledge.

Empirical Dynamic Modeling (EDM) is a nonlinear time series causal inference framework. The latest implementation of EDM, cppEDM, has only been used for small datasets due to computational cost. With the growth of data collection capabilities, there is a great need to identify causal relationships in large datasets. We present mpEDM, a parallel distributed implementation of EDM optimized for modern GPU-centric supercomputers. We improve the original algorithm to reduce redundant computation and optimize the implementation to fully utilize hardware resources such as GPUs and SIMD units. As a use case, we run mpEDM on AI Bridging Cloud Infrastructure (ABCI) using datasets of an entire animal brain sampled at single neuron resolution to identify dynamical causation patterns across the brain. mpEDM is 1,530× faster than cppEDM and a dataset containing 101,729 neuron was analyzed in 199 seconds on 512 nodes. This is the largest EDM causal inference achieved to date.