More Like this

1. Networks of Causal Linkage Between Eigenmodes Characterize Behavioral Dynamics of Caenorhabditis elegans

   https://doi.org/10.1371/journal.pcbi.1009329  

   Saberski, Erik ; Bock, Antonia K. ; Goodridge, Rachel ; Agarwal, Vitul ; Lorimer, Tom ; Rifkin, Scott A. ; Sugihara, George ( September 2021 , PLOS Computational Biology)

   Stephens, Greg J (Ed.)

   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. 

   more » « less
2. Discovering sparse interpretable dynamics from partial observations

   https://doi.org/10.1038/s42005-022-00987-z  

   Lu, Peter Y. ; Ariño Bernad, Joan ; Soljačić, Marin ( August 2022 , Communications Physics)

   Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems.

    

   more » « less
3. Discovering conservation laws using optimal transport and manifold learning

   https://doi.org/10.1038/s41467-023-40325-7  

   Lu, Peter Y. ; Dangovski, Rumen ; Soljačić, Marin ( August 2023 , Nature Communications)

   Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical information or rely on black box parametric deep learning methods. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach for discovering conserved quantities. We test this new approach on a variety of physical systems and demonstrate that our method is able to both identify the number of conserved quantities and extract their values. Using tools from optimal transport theory and manifold learning, our proposed method provides a direct geometric approach to identifying conservation laws that is both robust and interpretable without requiring an explicit model of the system nor accurate time information.

    

   more » « less
4. Foraging ecology drives social information reliance in an avian eavesdropping community

   https://doi.org/10.1002/ece3.5561  

   Jones, Harrison H. ; Sieving, Kathryn E. ( September 2019 , Ecology and Evolution)

   Vertebrates obtain social information about predation risk by eavesdropping on the alarm calls of sympatric species. In the Holarctic, birds in the family Paridae function as sentinel species; however, factors shaping eavesdroppers' reliance on their alarm calls are unknown. We compared three hypothesized drivers of eavesdropper reliance: (a) foraging ecology, (b) degree of sociality, and (c) call relevance (caller‐to‐eavesdropper body‐size difference). In a rigorous causal‐comparative design, we presented Tufted Titmouse (Baeolophus bicolor) alarm calls to 242 individuals of 31 ecologically diverse bird species in Florida forests and recorded presence/absence and type (diving for cover or freezing in place) of response. Playback response was near universal, as individuals responded to 87% of presentations (N = 211). As an exception to this trend, the sit‐and‐wait flycatcher Eastern Phoebe (Sayornis phoebe) represented 48% of the nonresponses. We tested 12 predictor variables representing measures relevant to the three hypothesized drivers, distance to playback speaker, and vulnerability at time of playback (eavesdropper's microhabitat when alarm call is detected). Using model‐averaged generalized linear models, we determined that foraging ecology best predicted playback response, with aerial foragers responding less often. Foraging ecology (distance from trunk) and microhabitat occupied during playback (distance to escape cover) best predicted escape behavior type. We encountered a sparsity of sit‐and‐wait flycatchers (3 spp.), yet their contrasting responses relative to other foraging behaviors clearly identified foraging ecology as a driver of species‐specific antipredator escape behavior. Our findings align well with known links between the exceptional visual acuity and other phenotypic traits of flycatchers that allow them to rely more heavily on personal rather than social information while foraging. Our results suggest that foraging ecology drives species‐specific antipredator behavior based on the availability and type of escape cover.

    

   more » « less
5. Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling

   Nassar, J. ; Linderman, S.W. ; Bugallo, M. ; Park, I.M. ( January 2019 , International Conference on Learning Representations (ICLR))

   Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability. 

   more » « less