arXiv subjects

Bingni W. Brunton

Publications and source records attributed to Bingni W. Brunton.

At least 19 recordsLinked to original sources

arXiv2026

MIMIC-MJX: Neuromechanical Emulation of Animal Behavior

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 biomechanically grounded neural control policies from kinematics. MIMIC-MJX provides a platform for modeling the generative process of motor control by training neural controllers that learn to actuate biomechanical animal models in physics simulation to reproduce real kinematic trajectories. We demonstrate that our implementation is accurate, fast, and generalizable to diverse animal body models, and that it can be trained with modest amounts of motion data. MIMIC-MJX can be used to model motor control policies and simulate behavioral experiments, illustrating its potential as an integrative modeling framework for neuroscience.

q-bio.NC↗

arXiv2025

Network inference via process motifs for lagged correlation in linear stochastic processes

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.

stat.ML↗

arXiv2025

PySensors 2.0: A Python Package for Sparse Sensor Placement

PySensors is a Python package for selecting and placing a sparse set of sensors for reconstruction and classification tasks. In this major update to PySensors, we introduce spatially constrained sensor placement capabilities, allowing users to enforce constraints such as maximum or exact sensor counts in specific regions, incorporate predetermined sensor locations, and maintain minimum distances between sensors. We extend functionality to support custom basis inputs, enabling integration of any data-driven or spectral basis. We also propose a thermodynamic approach that goes beyond a single "optimal" sensor configuration and maps the complete landscape of sensor interactions induced by the training data. This comprehensive view facilitates integration with external selection criteria and enables assessment of sensor replacement impacts. The new optimization technique also accounts for over- and under-sampling of sensors, utilizing a regularized least squares approach for robust reconstruction. Additionally, we incorporate noise-induced uncertainty quantification of the estimation error and provide visual uncertainty heat maps to guide deployment decisions. To highlight these additions, we provide a brief description of the mathematical algorithms and theory underlying these new capabilities. We demonstrate the usage of new features with illustrative code examples and include practical advice for implementation across various application domains. Finally, we outline a roadmap of potential extensions to further enhance the package's functionality and applicability to emerging sensing challenges.

cs.RO↗

arXiv2025

ODIN: Open Data In Neurophysiology: Advancements, Solutions & Challenges

Across the life sciences, an ongoing effort over the last 50 years has made data and methods more reproducible and transparent. This openness has led to transformative insights and vastly accelerated scientific progress. For example, structural biology and genomics have undertaken systematic collection and publication of protein sequences and structures over the past half-century, and these data have led to scientific breakthroughs that were unthinkable when data collection first began. We believe that neuroscience is poised to follow the same path, and that principles of open data and open science will transform our understanding of the nervous system in ways that are impossible to predict at the moment. To this end, new social structures along with active and open scientific communities are essential to facilitate and expand the still limited adoption of open science practices in our field. Unified by shared values of openness, we set out to organize a symposium for Open Data in Neuroscience (ODIN) to strengthen our community and facilitate transformative neuroscience research at large. In this report, we share what we learned during this first ODIN event. We also lay out plans for how to grow this movement, document emerging conversations, and propose a path toward a better and more transparent science of tomorrow.

q-bio.NC↗

arXiv2025

Decoding complexity: how machine learning is redefining scientific discovery

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.

cs.LG↗

arXiv2023

HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations

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.

cs.LG↗

arXiv2023

BKinD-3D: Self-Supervised 3D Keypoint Discovery from Multi-View Videos

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.

cs.CV↗

arXiv2022

Data-driven unsteady aeroelastic modeling for control

Aeroelastic structures, from insect wings to wind turbine blades, experience transient unsteady aerodynamic loads that are coupled to their motion. Effective real-time control of flexible structures relies on accurate and efficient predictions of both the unsteady aeroelastic forces and airfoil deformation. For rigid wings, classical unsteady aerodynamic models have recently been reformulated in state-space for control and extended to include viscous effects. Here we further extend this modeling framework to include the deformation of a flexible wing in addition to the quasi-steady, added mass, and unsteady viscous forces. We develop low-order linear models based on data from direct numerical simulations of flow past a flexible wing at low Reynolds number. We demonstrate the effectiveness of these models to track aggressive maneuvers with model predictive control while constraining maximum wing deformation. This system identification approach provides an interpretable, accurate, and low-dimensional representation of an aeroelastic system that can aid in system and controller design for applications where transients play an important role.

physics.flu-dyn↗

arXiv2022

Deep Neural Imputation: A Framework for Recovering Incomplete Brain Recordings

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.

cs.LG↗

arXiv2022

Neural-inspired Measurement Observability

The neural encoding by biological sensors of flying insects, which prefilters stimulus data before sending it to the central nervous system in the form of voltage spikes, enables sensing capabilities that are computationally low-cost while also being highly robust to noise. This process, which can be modeled as the composition of a linear moving average filter and a nonlinear decision function, inspired the work reported here to improve engineered sensing performance by maximizing the observability of particular neural-inspired composite measurement functions. We first present a tool to determine the observability of a linear system with measurement delay (the first element of the composition), then use a Lie algebraic observability approach to study nonlinear autonomous systems with output delay (the second element of the composition). The Lie algebraic tools are then extended to address overall observability of systems with composite outputs as in the neural encoder model we adopt. The analytical outcomes are supported using the empirical observability Gramian, and optimal sensor placement on a bioinspired wing model is performed using metrics based on the empirical Gramian.

eess.SY↗

arXiv2021

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world data sets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900-1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.

math.NA↗

arXiv2021

SINDy with Control: A Tutorial

Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.

math.OC↗

arXiv2021

PySensors: A Python Package for Sparse Sensor Placement

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.

eess.SP↗

arXiv2021

Structured Time-Delay Models for Dynamical Systems with Connections to Frenet-Serret Frame

Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode decomposition (DMD) on time-delay coordinates provide linear representations of strongly nonlinear systems, in the so-called Hankel alternative view of Koopman (HAVOK) approach. Curiously, the resulting linear model has a matrix representation that is approximately antisymmetric and tridiagonal with a zero diagonal; for chaotic systems, there is an additional forcing term in the last component. In this paper, we establish a new theoretical connection between HAVOK and the Frenet-Serret frame from differential geometry, and also develop an improved algorithm to identify more stable and accurate models from less data. In particular, we show that the sub- and super-diagonal entries of the linear model correspond to the intrinsic curvatures in Frenet-Serret frame. Based on this connection, we modify the algorithm to promote this antisymmetric structure, even in the noisy, low-data limit. We demonstrate this improved modeling procedure on data from several nonlinear synthetic and real-world examples.

math.DS↗

arXiv2021

Learning dominant physical processes with data-driven balance models

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

physics.flu-dyn↗

arXiv2020

Numerical differentiation of noisy data: A unifying multi-objective optimization framework

Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical formulation of numerical differentiation is typically ill-posed, and researchers often resort to an \textit{ad hoc} process for choosing one of many computational methods and its parameters. In this work, we take a principled approach and propose a multi-objective optimization framework for choosing parameters that minimize a loss function to balance the faithfulness and smoothness of the derivative estimate. Our framework has three significant advantages. First, the task of selecting multiple parameters is reduced to choosing a single hyper-parameter. Second, where ground-truth data is unknown, we provide a heuristic for automatically selecting this hyper-parameter based on the power spectrum and temporal resolution of the data. Third, the optimal value of the hyper-parameter is consistent across different differentiation methods, thus our approach unifies vastly different numerical differentiation methods and facilitates unbiased comparison of their results. Finally, we provide an extensive open-source Python library \texttt{pynumdiff} to facilitate easy application to diverse datasets (https://github.com/florisvb/PyNumDiff).

math.DS↗

arXiv2020

Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation

Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the actuations are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate causal reconstructions: Granger causality (GC) with perturbations, and our proposed perturbation cascade inference (PCI). Perturbed GC is capable of inferring smaller networks under low coupling strength regimes. Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (2-5 node) and large (10-20 node) networks, with both linear and nonlinear dynamics. Thus the ability to apply a large and diverse set of perturbations/actuations to the network is critical for successfully and accurately determining causal relations and disambiguating between various viable networks.

math.DS↗

arXiv2020

Investigating naturalistic hand movements by behavior mining in long-term video and neural recordings

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.

q-bio.NC↗