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.

Charles Y. Zhang, Yuanjia Yang, Aidan Sirbu et al.

The primary output of the nervous system is movement and behavior. While recent advances have democratized pose tracking during complex behavior, kinematic trajectories alone provide only indirect access to the underlying control processes. Here we present MIMIC-MJX, a framework for learning biologically-plausible neural control policies from kinematics. MIMIC-MJX models the generative process of motor control by training neural controllers that learn to actuate biomechanically-realistic body models in physics simulation to reproduce real kinematic trajectories. We demonstrate that our implementation is accurate, fast, data-efficient, and generalizable to diverse animal body models. Policies trained with MIMIC-MJX can be utilized to both analyze neural control strategies and simulate behavioral experiments, illustrating its potential as an integrative modeling framework for neuroscience.

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.

Krithika Manohar, Bingni W. Brunton, J. Nathan Kutz et al.

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent compressibility enables sparse sensing. This article explores optimized sensor placement for signal reconstruction based on a tailored library of features extracted from training data. Sparse point sensors are discovered using the singular value decomposition and QR pivoting, which are two ubiquitous matrix computations that underpin modern linear dimensionality reduction. Sparse sensing in a tailored basis is contrasted with compressed sensing, a universal signal recovery method in which an unknown signal is reconstructed via a sparse representation in a universal basis. Although compressed sensing can recover a wider class of signals, we demonstrate the benefits of exploiting known patterns in data with optimized sensing. In particular, drastic reductions in the required number of sensors and improved reconstruction are observed in examples ranging from facial images to fluid vorticity fields. Principled sensor placement may be critically enabling when sensors are costly and provides faster state estimation for low-latency, high-bandwidth control. MATLAB code is provided for all examples.

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.