Bingni W. Brunton

Jennifer J. Sun, Lili Karashchuk, Amil Dravid et al. · cambridge, uw

Quantifying motion in 3D is important for studying the behavior of humans and other animals, but manual pose annotations are expensive and time-consuming to obtain. Self-supervised keypoint discovery is a promising strategy for estimating 3D poses without annotations. However, current keypoint discovery approaches commonly process single 2D views and do not operate in the 3D space. We propose a new method to perform self-supervised keypoint discovery in 3D from multi-view videos of behaving agents, without any keypoint or bounding box supervision in 2D or 3D. Our method, BKinD-3D, uses an encoder-decoder architecture with a 3D volumetric heatmap, trained to reconstruct spatiotemporal differences across multiple views, in addition to joint length constraints on a learned 3D skeleton of the subject. In this way, we discover keypoints without requiring manual supervision in videos of humans and rats, demonstrating the potential of 3D keypoint discovery for studying behavior.

Mozes Jacobs, Bingni W. Brunton, Steven L. Brunton et al. · uw

The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of interpretable models in the form of sparse, deterministic governing laws. Recent works have sought to adapt this approach to the stochastic setting, though these adaptations are severely hampered by the curse of dimensionality. On the other hand, Bayesian-inspired deep learning methods have achieved widespread success in high-dimensional probabilistic modeling via computationally efficient approximate inference techniques, suggesting the use of these techniques for efficient stochastic equation discovery. Here, we introduce HyperSINDy, a framework for modeling stochastic dynamics via a deep generative model of sparse governing equations whose parametric form is discovered from data. HyperSINDy employs a variational encoder to approximate the distribution of observed states and derivatives. A hypernetwork \citep{ha_hypernetworks_2016} transforms samples from this distribution into the coefficients of a differential equation whose sparse form is learned simultaneously using a trainable binary mask \citep{louizos_learning_2018}. Once trained, HyperSINDy generates stochastic dynamics via a differential equation whose coefficients are driven by a Gaussian white noise. In experiments, HyperSINDy accurately recovers ground truth stochastic governing equations, with learned stochasticity scaling to match that of the data. Finally, HyperSINDy provides uncertainty quantification that scales to high-dimensional systems. Taken together, HyperSINDy offers a promising framework for model discovery and uncertainty quantification in real-world systems, integrating sparse equation discovery methods with advances in statistical machine learning and deep generative modeling.

Seth M. Hirsh, Bingni W. Brunton, J. Nathan Kutz · uw

We propose a new solution to the blind source separation problem that factors mixed time-series signals into a sum of spatiotemporal modes, with the constraint that the temporal components are intrinsic mode functions (IMF's). The key motivation is that IMF's allow the computation of meaningful Hilbert transforms of non-stationary data, from which instantaneous time-frequency representations may be derived. Our spatiotemporal intrinsic mode decomposition (STIMD) method leverages spatial correlations to generalize the extraction of IMF's from one-dimensional signals, commonly performed using the empirical mode decomposition (EMD), to multi-dimensional signals. Further, this data-driven method enables future-state prediction. We demonstrate STIMD on several synthetic examples, comparing it to common matrix factorization techniques, namely singular value decomposition (SVD), independent component analysis (ICA), and dynamic mode decomposition (DMD). We show that STIMD outperforms these methods at reconstruction and extracting interpretable modes. Next, we apply STIMD to analyze two real-world datasets, gravitational wave data and neural recordings from the rodent hippocampus.

Sabera Talukder, Jennifer J. Sun, Matthew Leonard et al. · uw

Neuroscientists and neuroengineers have long relied on multielectrode neural recordings to study the brain. However, in a typical experiment, many factors corrupt neural recordings from individual electrodes, including electrical noise, movement artifacts, and faulty manufacturing. Currently, common practice is to discard these corrupted recordings, reducing already limited data that is difficult to collect. To address this challenge, we propose Deep Neural Imputation (DNI), a framework to recover missing values from electrodes by learning from data collected across spatial locations, days, and participants. We explore our framework with a linear nearest-neighbor approach and two deep generative autoencoders, demonstrating DNI's flexibility. One deep autoencoder models participants individually, while the other extends this architecture to model many participants jointly. We evaluate our models across 12 human participants implanted with multielectrode intracranial electrocorticography arrays; participants had no explicit task and behaved naturally across hundreds of recording hours. We show that DNI recovers not only time series but also frequency content, and further establish DNI's practical value by recovering significant performance on a scientifically-relevant downstream neural decoding task.

Alice C. Schwarze, Sara M. Ichinaga, Bingni W. Brunton · uw

A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose to infer networks of causal relations via pairwise edge measure (PEMs) that one can easily compute from lagged correlation matrices. Motivated by contributions of process motifs to covariance and lagged variance, we formulate two PEMs that correct for confounding factors and for reverse causation. To demonstrate the performance of our PEMs, we consider network interference from simulations of linear stochastic processes, and we show that our proposed PEMs can infer networks accurately and efficiently. Specifically, for slightly autocorrelated time-series data, our approach achieves accuracies higher than or similar to Granger causality, transfer entropy, and convergent crossmapping -- but with much shorter computation time than possible with any of these methods. Our fast and accurate PEMs are easy-to-implement methods for network inference with a clear theoretical underpinning. They provide promising alternatives to current paradigms for the inference of linear models from time-series data, including Granger causality, vector-autoregression, and sparse inverse covariance estimation.

Brian M. de Silva, Krithika Manohar, Emily Clark et al.

PySensors is a Python package for selecting and placing a sparse set of sensors for classification and reconstruction tasks. Specifically, PySensors implements algorithms for data-driven sparse sensor placement optimization for reconstruction (SSPOR) and sparse sensor placement optimization for classification (SSPOC). In this work we provide a brief description of the mathematical algorithms and theory for sparse sensor optimization, along with an overview and demonstration of the features implemented in PySensors (with code examples). We also include practical advice for user and a list of potential extensions to PySensors. Software is available at https://github.com/dynamicslab/pysensors.

Ricardo Vinuesa, Paola Cinnella, Jean Rabault et al. · uw

As modern scientific instruments generate vast amounts of data and the volume of information in the scientific literature continues to grow, machine learning (ML) has become an essential tool for organising, analysing, and interpreting these complex datasets. This paper explores the transformative role of ML in accelerating breakthroughs across a range of scientific disciplines. By presenting key examples -- such as brain mapping and exoplanet detection -- we demonstrate how ML is reshaping scientific research. We also explore different scenarios where different levels of knowledge of the underlying phenomenon are available, identifying strategies to overcome limitations and unlock the full potential of ML. Despite its advances, the growing reliance on ML poses challenges for research applications and rigorous validation of discoveries. We argue that even with these challenges, ML is poised to disrupt traditional methodologies and advance the boundaries of knowledge by enabling researchers to tackle increasingly complex problems. Thus, the scientific community can move beyond the necessary traditional oversimplifications to embrace the full complexity of natural systems, ultimately paving the way for interdisciplinary breakthroughs and innovative solutions to humanity's most pressing challenges.

Satpreet Harcharan Singh, Floris van Breugel, Rajesh P. N. Rao et al.

Tracking a turbulent plume to locate its source is a complex control problem because it requires multi-sensory integration and must be robust to intermittent odors, changing wind direction, and variable plume statistics. This task is routinely performed by flying insects, often over long distances, in pursuit of food or mates. Several aspects of this remarkable behavior have been studied in detail in many experimental studies. Here, we take a complementary in silico approach, using artificial agents trained with reinforcement learning to develop an integrated understanding of the behaviors and neural computations that support plume tracking. Specifically, we use deep reinforcement learning (DRL) to train recurrent neural network (RNN) agents to locate the source of simulated turbulent plumes. Interestingly, the agents' emergent behaviors resemble those of flying insects, and the RNNs learn to represent task-relevant variables, such as head direction and time since last odor encounter. Our analyses suggest an intriguing experimentally testable hypothesis for tracking plumes in changing wind direction -- that agents follow local plume shape rather than the current wind direction. While reflexive short-memory behaviors are sufficient for tracking plumes in constant wind, longer timescales of memory are essential for tracking plumes that switch direction. At the level of neural dynamics, the RNNs' population activity is low-dimensional and organized into distinct dynamical structures, with some correspondence to behavioral modules. Our in silico approach provides key intuitions for turbulent plume tracking strategies and motivates future targeted experimental and theoretical developments.

Satpreet H. Singh, Steven M. Peterson, Rajesh P. N. Rao et al.

Recent technological advances in brain recording and artificial intelligence are propelling a new paradigm in neuroscience beyond the traditional controlled experiment. Rather than focusing on cued, repeated trials, naturalistic neuroscience studies neural processes underlying spontaneous behaviors performed in unconstrained settings. However, analyzing such unstructured data lacking a priori experimental design remains a significant challenge, especially when the data is multi-modal and long-term. Here we describe an automated approach for analyzing simultaneously recorded long-term, naturalistic electrocorticography (ECoG) and naturalistic behavior video data. We take a behavior-first approach to analyzing the long-term recordings. Using a combination of computer vision, discrete latent-variable modeling, and string pattern-matching on the behavioral video data, we find and annotate spontaneous human upper-limb movement events. We show results from our approach applied to data collected for 12 human subjects over 7--9 days for each subject. Our pipeline discovers and annotates over 40,000 instances of naturalistic human upper-limb movement events in the behavioral videos. Analysis of the simultaneously recorded brain data reveals neural signatures of movement that corroborate prior findings from traditional controlled experiments. We also prototype a decoder for a movement initiation detection task to demonstrate the efficacy of our pipeline as a source of training data for brain-computer interfacing applications. Our work addresses the unique data analysis challenges in studying naturalistic human behaviors, and contributes methods that may generalize to other neural recording modalities beyond ECoG. We publicly release our curated dataset, providing a resource to study naturalistic neural and behavioral variability at a scale not previously available.

Kameron Decker Harris, Aleksandr Aravkin, Rajesh Rao et al.

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized by a system matrix, and we model this stack of potentially different system matrices as a low rank tensor. Because of its structure, the model is scalable to high-dimensional data and can easily incorporate priors such as smoothness over time. We find the components of the tensor using alternating minimization and prove that any stationary point of this algorithm is a local minimum. We demonstrate on a synthetic example that our method identifies the true rank of a switching linear system in the presence of noise. We illustrate our model's utility and superior scalability over extant methods when applied to several synthetic and real-world example: two types of time-varying linear systems, worm behavior, sea surface temperature, and monkey brain datasets.

Nancy Xin Ru Wang, Ali Farhadi, Rajesh Rao et al.

Developing useful interfaces between brains and machines is a grand challenge of neuroengineering. An effective interface has the capacity to not only interpret neural signals, but predict the intentions of the human to perform an action in the near future; prediction is made even more challenging outside well-controlled laboratory experiments. This paper describes our approach to detect and to predict natural human arm movements in the future, a key challenge in brain computer interfacing that has never before been attempted. We introduce the novel Annotated Joints in Long-term ECoG (AJILE) dataset; AJILE includes automatically annotated poses of 7 upper body joints for four human subjects over 670 total hours (more than 72 million frames), along with the corresponding simultaneously acquired intracranial neural recordings. The size and scope of AJILE greatly exceeds all previous datasets with movements and electrocorticography (ECoG), making it possible to take a deep learning approach to movement prediction. We propose a multimodal model that combines deep convolutional neural networks (CNN) with long short-term memory (LSTM) blocks, leveraging both ECoG and video modalities. We demonstrate that our models are able to detect movements and predict future movements up to 800 msec before movement initiation. Further, our multimodal movement prediction models exhibit resilience to simulated ablation of input neural signals. We believe a multimodal approach to natural neural decoding that takes context into account is critical in advancing bioelectronic technologies and human neuroscience.

Jing Wu, Benjamin R. Shuman, Bingni W. Brunton et al.

Neural correlates of movement planning onset and direction may be present in human electrocorticography in the signal dynamics of both motor and non-motor cortical regions. We use a three-stage model of jPCA reduced-rank hidden Markov model (jPCA-RR-HMM), regularized shrunken-centroid discriminant analysis (RDA), and LASSO regression to extract direction-sensitive planning information and movement onset in an upper-limb 3D isometric force task in a human subject. This mode achieves a relatively high true positive force-onset prediction rate of 60% within 250ms, and an above-chance 36% accuracy (17% chance) in predicting one of six planned 3D directions of isometric force using pre-movement signals. We also find direction-distinguishing information up to 400ms before force onset in the pre-movement signals, captured by electrodes placed over the limb-ipsilateral dorsal premotor regions. This approach can contribute to more accurate decoding of higher-level movement goals, at earlier timescales, and inform sensor placement. Our results also contribute to further understanding of the spatiotemporal features of human motor planning.

B. W. Brunton, S. L. Brunton, J. L. Proctor et al.

The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude sparser still. We define enhanced sparsity as the reduction in number of measurements required for classification over reconstruction. In this work, we exploit enhanced sparsity and learn spatial sensor locations that optimally inform a categorical decision. The algorithm solves an l1-minimization to find the fewest entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space. Once the sensor locations have been identified from the training data, subsequent test samples are classified with remarkable efficiency, achieving performance comparable to that obtained by discrimination using the full image. Sensor locations may be learned from full images, or from a random subsample of pixels. For classification between more than two categories, we introduce a coupling parameter whose value tunes the number of sensors selected, trading accuracy for economy. We demonstrate the algorithm on example datasets from image recognition using PCA for feature extraction and LDA for discrimination; however, the method can be broadly applied to non-image data and adapted to work with other methods for feature extraction and discrimination.