Machine Learning

UW Data Science Seminar with Megan Ebers

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Title slide from the UW eScience Data Science seminar that says "Mobile sensing with shallow recurrent decoder networks. Megan R. Ebers"

Steele lab member and postdoctoral scholar, Megan Ebers, was featured in the Winter 2024 UW Data Science Seminar series. You can watch her full presentation on “Mobile sensing with shallow recurrent decoder networks” linked HERE on UW eScience Institute’s YouTube channel.

Abstract: Sensing is a fundamental task for the monitoring, forecasting, and control of complex systems. In many applications, a limited number of sensors are available and must move with the dynamics, such as with wearable technology or ocean monitoring buoys. In these dynamic systems, the sensors’ time history encodes a significant amount of information that can be extracted for critical tasks. We show that by leveraging the time-history of a sparse set of sensors, we can encode global information of the measured high-dimensional system using shallow recurrent decoder networks. This paradigm has important applications for technical challenges in climate modeling, natural disaster evaluation, and personalized health monitoring; we focus especially on how this paradigm has the potential to transform the way we monitor and manage movement-related health outcomes.

Bio: Megan Ebers is a postdoctoral scholar in applied mathematics with UW’s NSF AI Institute in Dynamic Systems. In her PhD research, she developed and applied machine learning methods for dynamics systems to understand and enable human mobility. Her postdoctoral research focuses on data-driven and reduced-order methods for complex systems, so as to continue her work in human-centered research challenges, as well as to extend her research to a broader set of technical challenges, including turbulent flow modeling, natural disaster monitoring, and acoustic object detection.

MR Ebers, KM Steele, JN Kutz (2024) “Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects”

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Journal Article in SIAM Journal on Applied Dynamical Systems

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms.

Top panel: An approximate dynamical model f(·) provides estimates of system behavior used for both reconstruction and forecasting (shaded region), x(t). However, true behavior x0(t) (without observation noise) deviates from these estimates. The goal of discrepancy modeling is to learn a discrepancy model that recovers the missing physics and augments the approximate dynamics to improve system characterization, ˜x(t). Bottom panel: There are two approaches for building a discrepancy model to estimate missing physics: (i) modeling systematic state-space residual between the approximate state space, x(t), and true state space, x0(t), and (ii) learning the deterministic dynamical error between the true dynamics, x˙ 0(t) = f(x0(t)) + g(x0(t)), and the approximate dynamics, x˙ (t) = f(x(t)). In real-world systems, the true system behavior is noisily observed, yk = x0(tk) + N(μ, σ), model-measurement mismatch contains both deterministic and random effects; measurements yk = y(kΔt) denote a continuous dynamical system’s full state noisily observed at discrete time points.

Aim: Introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used.

Method: Specifically, we use four fundamentally different methods to demonstrate the mathematical implementations of discrepancy modeling: (i) the sparse identification of nonlinear dynamics (SINDy), (ii) dynamic mode decomposition (DMD), (iii) Gaussian process regression (GPR), and (iv) neural networks (NN). The choice of method depends on one’s intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., state- or dynamical-space operability).

Results: We demonstrate the utility and suitability for both discrepancy modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type.

Interpretation: In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.

SWE 2023

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Tori and Charlotte are standing with a large sign that says "Heart LA"

Congratulations to Charlotte Caskey and Victoria (Tori) Landrum for presenting as finalists in the Collegiate Poster Competition at the Society of Women Engineer’s Annual Conference in LA this weekend.

Tori placed 3rd in the undergraduate student division for her poster titled “Spinal Stimulation Improves Spasticity and Motor Control in Children with Cerebral Palsy”. Charlotte placed 1st in the graduate student division for her work titled “Machine Learning for Quantifying Rehabilitation Response in Children with Cerebral Palsy.

Congratulations, Charlotte and Tori!

Tori and Charlotte are standing outside of a convention center with a large sign that says "Welcome to SWE 23"
Charlotte has long brown hair and is wearing glasses, a black blazer and black pants. She is standing in front of her poster at SWE.
Vitoria (Tori) has short blonde hair and is wearing a black shirt and grey pant. Tori is standing in front of a poster at SWE 2023.

AM Spomer, RZ Yan, MH Schwartz, KM Steele (2023) “Motor control complexity can be dynamically simplified during gait pattern exploration using motor control-based biofeedback”

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Journal Article in Journal of Neurophysiology

Understanding how the central nervous system coordinates diverse motor outputs has been a topic of extensive investigation. Although it is generally accepted that a small set of synergies underlies many common activities, such as walking, whether synergies are equally robust across a broader array of gait patterns or can be flexibly modified remains unclear.

Schematic of the custom biofeedback system. A) Motor control biofeedback used to encourage pattern exploration. B) Individuals significantly modified motor control complexity using biofeedback. C) Distal gait mechanics were associated with changes in control complexity.Aim: The aim of this study was to characterize the robustness of synergies to changing biomechanical constraints during walking. Specifically, we evaluated the extent to which nondisabled individuals could modulate both synergy structure and complexity while using motor control biofeedback to drive broad gait pattern exploration.

Methods: We evaluated the extent to which synergies changed as nondisabled adults (n = 14) explored gait patterns using custom biofeedback. Secondarily, we used Bayesian additive regression trees to identify factors that were associated with synergy modulation.

Results: Participants explored 41.1 ± 8.0 gait patterns using biofeedback, during which synergy recruitment changed depending on the type and magnitude of gait pattern modification. Specifically, a consistent set of synergies was recruited to accommodate small deviations from baseline, but additional synergies emerged for larger gait changes. Synergy complexity was similarly modulated; complexity decreased for 82.6% of the attempted gait patterns, but distal gait mechanics were strongly associated with these changes. In particular, greater ankle dorsiflexion moments and knee flexion through stance, as well as greater knee extension moments at initial contact, corresponded to a reduction in synergy complexity.

Interpretation: Taken together, these results suggest that the central nervous system preferentially adopts a low-dimensional, largely invariant control strategy but can modify that strategy to produce diverse gait patterns. Beyond improving understanding of how synergies are recruited during gait, study outcomes may also help identify parameters that can be targeted with interventions to alter synergies and improve motor control after neurological injury.

New & Noteworthy: We used a motor control-based biofeedback system and machine learning to characterize the extent to which nondisabled adults can modulate synergies during gait pattern exploration. Results revealed that a small library of synergies underlies an array of gait patterns but that recruitment from this library changes as a function of the imposed biomechanical constraints. Our findings enhance understanding of the neural control of gait and may inform biofeedback strategies to improve synergy recruitment after neurological injury.

KM Steele, MH Schwartz (2022) “Causal Effects of Motor Control on Gait Kinematics After Orthopedic Surgery in Cerebral Palsy: A Machine-Learning Approach”

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Journal Article in Frontiers in Human Neuroscience

Altered motor control is common in cerebral palsy (CP). Understanding how altered motor control affects movement and treatment outcomes is important but challenging due to complex interactions with other neuromuscular impairments. While regression can be used to examine associations between impairments and movement, causal modeling provides a mathematical framework to specify assumed causal relationships, identify covariates that may introduce bias, and test model plausibility.

FIGURE 1 Directed Acyclic Graph (DAG) describing the assumed causal relationships between SEMLS (exposure) and 1GDI (outcome). The causal relationship between SEMLS and 1GDI is mediated by changes in impairments (1Imp). Baseline GDI (GDIpre) and 1GDI are related by measurement methods and other, unmeasured factors. Baseline impairment (Imppre), surgical history (Hx), and Age are also included as causal factors. The DAG also includes unmeasured factors related to general CP severity, which impact baseline impairment and surgical history. The step-by-step process and rationale for this DAG are available in the Supplementary Material and an interactive version is available on dagitty (http://dagitty.net/mUCSPWo).Aim: The goal of this research was to quantify the causal effects of altered motor control and other impairments on gait, before and after single-event multi-level orthopedic surgery (SEMLS).

Methods: We evaluated the impact of SEMLS on change in Gait Deviation Index (ΔGDI) between gait analyses. We constructed our causal model with a Directed Acyclic Graph that included the assumed causal relationships between SEMLS, ΔGDI, baseline GDI (GDIpre), baseline neurologic and orthopedic impairments (Imppre), age, and surgical history. We identified the adjustment set to evaluate the causal effect of SEMLS on ΔGDI and the impact of Imppre on ΔGDI and GDIpre. We used Bayesian Additive Regression Trees (BART) and accumulated local effects to assess relative effects.

Results: We prospectively recruited a cohort of children with bilateral CP undergoing SEMLS (N = 55, 35 males, age: 10.5 ± 3.1 years) and identified a control cohort with bilateral CP who did not undergo SEMLS (N = 55, 30 males, age: 10.0 ± 3.4 years). There was a small positive causal effect of SEMLS on ΔGDI (1.70 GDI points). Altered motor control (i.e., dynamic and static motor control) and strength had strong effects on GDIpre, but minimal effects on ΔGDI. Spasticity and orthopedic impairments had minimal effects on GDIpre or ΔGDI.

Interpretation: Altered motor control did have a strong effect on GDIpre, indicating that these impairments do have a causal effect on a child’s gait pattern, but minimal effect on expected changes in GDI after SEMLS. Heterogeneity in outcomes suggests there are other factors contributing to changes in gait. Identifying these factors and employing causal methods to examine the complex relationships between impairments and movement will be required to advance our understanding and care of children with CP.