About

Richard B. Sowers is a professor at the University of Illinois whose work spans engineering and mathematics, focusing on quantitative thinking and handling large amounts of data to address complex real-world problems. His research includes diagnosing medical conditions such as Multiple Sclerosis through gait pattern analysis, optimizing scheduling in smart homes to balance efficiency and frugality, and studying traffic congestion patterns using topological methods. He also investigates routing strategies in urban environments to understand tradeoffs between travel time and accident avoidance. In the field of precision agriculture, Sowers develops algorithmic geolocation techniques for hand-picked crops to monitor and optimize harvests, as well as models to minimize spoilage in high-value specialty crops during post-harvest handling. His work extends to financial engineering and mathematics, where he applies uncertainty quantification methods from engineering to measure economic uncertainty and analyze dynamics in bankrupt stocks. Additionally, he explores stochastic moving boundary problems in pure mathematics, studying the effects of noise on multiphase system dynamics. Sowers' interdisciplinary research is supported by various sponsors and partners, including government agencies and research institutes, reflecting a broad impact across multiple domains.

Research topics

• Artificial Intelligence
• Machine Learning
• Computer Science
• Medicine
• Physical medicine and rehabilitation
• Mathematics
• Engineering
• Algorithm
• Real-time computing
• Physical therapy
• Operating system
• Mathematical optimization

Selected publications

• Extending Anxiety Detection from Multimodal Wearables in Controlled Conditions to Real-World Environments

  Sensors · 2025-02-18 · 10 citations

  articleOpen access

  This study quantitatively evaluated whether and how machine learning (ML) models built by data from controlled conditions can fit real-world conditions. This study focused on feature-based models using wearable technology from real-world data collected from young adults, so as to provide insights into the models' robustness and the specific challenges posed by diverse environmental noise. Feature-based models, particularly XGBoost and Decision Trees, demonstrated considerable resilience, maintaining higher accuracy and reliability across different noise levels. This investigation included an in-depth analysis of transfer learning, highlighting its potential and limitations in adapting models developed from standard datasets, like WESAD, to complex real-world scenarios. Moreover, this study analyzed the distributed feature importance across various physiological signals, such as electrodermal activity (EDA) and electrocardiography (ECG), considering their vulnerability to environmental factors. It was found that integrating multiple physiological data types could significantly enhance model robustness. The results underscored the need for a nuanced understanding of signal contributions to model efficacy, suggesting that feature-based models showed much promise in practical applications.

  PublisherOA PDFDOI

• Continuous Heart Rate Recovery Monitoring With ECG Signals From Wearables: Identifying Risk Groups in the General Population

  IEEE Journal of Biomedical and Health Informatics · 2025-03-11 · 2 citations

  articleOpen access

  Heart rate recovery (HRR) is a critical indicator of cardiovascular fitness and autonomic nervous system function, reflecting the balance between sympathetic and parasympathetic activity. Slower HRR is often linked to cardiovascular and metabolic disorders, highlighting its potential for identifying high-risk individuals. In this study, we developed a feature engineering approach integrated to wearable device data to classify individuals into high-risk (slower HRR) and low-risk (faster HRR) groups. Data were collected from 38 participants (aged 20 to 76 years, 55.26% women) during treadmill trial, with ECG signals recorded using a smart shirt. Participants with an HRR equal to 28 beats per minute or below were classified as high-risk. Using machine learning classifiers, our approach achieved an area under the curve (AUC) score of 86% with Support Vector Classifier (SVC), demonstrating the feasibility of continuous heart health monitoring via wearable devices. Interestingly, age did not emerge as a significant predictor of HRR in our analysis, possibly due to the impact of lifestyle changes during the lockdown policy of COVID-19 era. This method holds promise for improving cardiovascular health monitoring accessibility and could support physicians in risk assessment and clinical decision-making.

  PublisherDOI

• Side boundary potentials for a Kolmogorov-type PDE

  Journal of Evolution Equations · 2025-10-10

  articleOpen access1st authorCorresponding

  Abstract We solve a Kolmogorov-type parabolic partial differential equation with a “side” boundary condition (in the direction of the weak Hörmander condition). We construct an approximate boundary potential which captures the effect of the boundary condition. Integrals against this approximate boundary potential have a novel jump discontinuity at the boundary which includes a measure discovered by McKean. We introduce some polynomial corrections to this approximate boundary potential and then construct a boundary-domain Volterra equation to solve the original partial differential equation. This Volterra integral equation is iteratively solved, and the bounds contain a periodic behavior resulting from the boundary effects. We discuss some applications to a problem of McKean.

  PublisherOA PDFDOI

• Review of ML Approaches in Anxiety Detection from In-Lab to In-the-Wild

  Preprints.org · 2025-07-28

  preprintOpen access

  This review provides a detailed exploration of the current state of anxiety detection using machine learning (ML), with a focus on both feature-based and end-to-end models. The field has experienced rapid growth, with a significant increase in academic output ne-cessitating an updated review of commonly used ML models and their performance, anxiety-inducing methodologies, data collection conditions, and dataset utilization. Feature-based ML models, such as Support Vector Machines, have been extensively employed due to their interpretability and simplicity. However, these models require manual feature engineering, which can be labor-intensive and potentially biased. End-to-end deep learning models have emerged as powerful alternatives, capable of utilizing raw signal directly and handling large datasets. Additionally, this review categorizes stressors into six distinct types – social, mental, physical, emotional, driving, and daily-life stressors – to provide a better overview of methodologies used to elicit anxiety. These are further explored based on whether data were collected under con-trolled in-lab conditions or real world in-the-wild conditions. This review underscores the need for further exploration into model architecture and their suitability for different types of data, advocating for a more nuanced and personalized approach to anxiety detection using machine learning.

  PublisherOA PDFDOI

• Scoping Review of ML Approaches in Anxiety Detection from In-Lab to In-the-Wild

  Applied Sciences · 2025-09-16 · 2 citations

  articleOpen access

  The field of anxiety detection and use of machine learning (ML) has experienced rapid growth necessitating an updated review of commonly used ML models and their performance, anxiety-inducing methodologies, data collection conditions, and dataset utilization. Feature-based ML models have been extensively employed due to their interpretability and simplicity. However, these models require manual feature engineering, which can be labor-intensive and potentially biased. End-to-end deep learning models have emerged as alternatives, capable of utilizing raw signal directly and handling large datasets. This review aims to provide a detailed exploration of anxiety detection using ML, including use of feature-based vs. end-to-end models, a taxonomy of stressors, performance benchmarks, challenges in deployment to real-world scenarios, and generalizability of findings, given limitations in sociodemographic diversity and heterogeneity in the use of validated anxiety measures. A total of 105 eligible papers were retrieved from the Scopus, IEEE Xplore, and PubMed databases. Stressors were categorized into six distinct types—social, mental, physical, emotional, driving, and daily-life stressors—to provide a better overview of methodologies used to elicit anxiety. Papers were organized according to the type of data collection—lab-based or real-world conditions—and characterized through the type of anxiety instrument used, population examined, and classification performance. This review underscores the need for further investigation into model architecture and their suitability for different types of data, limitations in population diversity and representation in existing studies, and advocating for a more nuanced and personalized approach to anxiety detection using machine learning.

  PublisherOA PDFDOI

• Comparative Analysis of Physiological and Speech Signals for State Anxiety Detection in University Students in STEM

  IEEE Transactions on Affective Computing · 2025-01-01

  article

  Anxiety is a common mental health condition that can significantly impair daily functioning, especially for university students in STEM. State anxiety is a situational emotional response and is typically assessed through self-reported questionnaires and clinical interviews. These traditional methods only capture discrete snapshots of an individual's emotional state and rely heavily on retrospective reporting. To overcome the limitations of self-reporting, we use wearable and contactless sensors. We continuously monitor a set of physiological signals (electrodermal activity (EDA), blood volume pulse (BVP), heart rate variability (HRV), and skin temperature (TEMP)) along with a behavioral signal (Speech) to detect state anxiety in real-time. We evaluate the predictive capabilities of these signals concerning self-reported anxiety levels, as measured by the six-item State-Trait Anxiety Inventory (STAI-6). Machine learning (ML) models are employed to classify participants into state anxiety risk groups based on two thresholds: clinical (STAI-6 score <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gt $</tex-math></inline-formula> 15) and median-based (STAI-6 score <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gt $</tex-math></inline-formula> median). Our results indicate that BVP outperforms other single modalities across classifiers, particularly when combined with TEMP, achieving true positive rates (TPRs) up to 0.90 under the median threshold. Additionally, speech features demonstrate competitive performance in certain conditions, while EDA, TEMP, and HRV exhibit greater variability. We believe that this study supports using wearables to monitor state anxiety.

  PublisherDOI

• Koopman representations with irregular time intervals

  Physica D Nonlinear Phenomena · 2025-12-01

  articleOpen accessSenior author

  • We propose a framework to recover Koopman eigenfunctions and eigenvalues for irregularly sampled data. • We show that a Koopman eigenfunction and eigenvalue can be recovered via a natural optimization problem. • We provide technical remarks on the anticipated challenge in optimization and suggest a procedure to address them. • Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. • Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction-recovery accuracy. Koopman operator theory has been widely applied to data assimilation problems of real systems governed by dynamics, as the theory allows for data-driven construction of modes of dynamical systems. In many modern problems, these modes often must be learned from data with irregular sampling intervals, as opposed to commonly used regularly sampled data. Here, we propose a framework to recover a Koopman eigenfunction–eigenvalue pair for irregularly sampled data. We show that a Koopman eigenpair can be recovered via a natural optimization problem. We provide technical remarks on the anticipated challenges in optimization and suggest a procedure to address them. Simulation studies under different irregular sampling scenarios verify the robustness of the proposed method in learning Koopman eigenfunctions. Compared with extended dynamic mode decomposition on data resampled via interpolation, our method shows improved eigenfunction–recovery accuracy.

  PublisherDOI

• On the Enumeration of all Unique Paths of Recombining Trinomial Trees

  ArXiv.org · 2025-10-03

  preprintOpen accessSenior author

  Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$ trajectories, making exhaustive enumeration infeasible. Under time-homogeneous dynamics, however, the graph exhibits two exploitable symmetries: (i) translational invariance of nodes and (ii) a canonical bijection between admissible paths and ordered tuples encoding weak compositions. Leveraging these, we introduce a mass-shifting enumeration algorithm that slides integer "masses" through a cardinality tuple to generate exactly one representative per path-equivalence class while implicitly counting the associated weak compositions. This trims the search space by an exponential factor, enabling markedly deeper trees -- and therefore tighter numerical approximations of the underlying evolution -- to be processed in practice. We further derive an upper bound on the combinatorial counting expression that induces a theoretical lower bound on the algorithmic cost of approximately $\mathcal{O}\bigl(D^{1/2}1.612^{D}\bigr)$. This correspondence permits direct benchmarking while empirical tests, whose pseudo-code we provide, corroborate the bound, showing only a small constant overhead and substantial speedups over classical breadth-first traversal. Finally, we highlight structural links between our algorithmic/combinatorial framework and Motzkin paths with Narayana-type refinements, suggesting refined enumerative formulas and new potential analytic tools for path-dependent functionals.

  PublisherOA PDFDOI

• Objective anxiety level classification using unsupervised learning and multimodal physiological signals

  Smart Health · 2025-03-29 · 2 citations

  article
  PublisherDOI

• Resilience of Machine Learning Models in Anxiety Detection: Assessing the Impact of Gaussian Noise on Wearable Sensors

  Applied Sciences · 2024-12-26 · 6 citations

  articleOpen access

  The resilience of machine learning models for anxiety detection through wearable technology was explored. The effectiveness of feature-based and end-to-end machine learning models for anxiety detection was evaluated under varying conditions of Gaussian noise. By adding synthetic Gaussian noise to a well-known open access affective states dataset collected with commercially available wearable devices (WESAD), a performance baseline was established using the original dataset. This was followed by an examination of the impact of noise on model accuracy to better understand model performance (F1-score and Accuracy) changes as a function of noise. The results of the analysis revealed that with the increase in noise, the performance of feature-based models dropped from a high of 90% F1-score and 92% accuracy to 65% and 70%, respectively; while end-to-end models showed a decrease from an 85% F1-score and 87% accuracy to below 60% and 65%, respectively. This indicated a proportional decline in performance across both feature-based and end-to-end models as noise levels increased, challenging initial assumptions about model resilience. This analysis highlights the need for more robust algorithms capable of maintaining accuracy in noisy, real-world environments and emphasizes the importance of considering environmental factors in the development of wearable anxiety detection systems.

  PublisherOA PDFDOI

Recent grants

• Random Perturbations of Complex Dynamical Systems

  NSF · $193k · 2003–2007

• AMC-SS: Noise-Induced Transitions in Multiscale Systems

  NSF · $130k · 2006–2010

• Signatures and Barcodes: Data-driven Understanding of Transportation System Performance during Extreme Events

  NSF · $500k · 2017–2021

• BECS: Rare Systematic Risk in Markets: Modelling, Theory and Computation

  NSF · $310k · 2010–2015

• I-Corps: Data Analytics for Hand-Picked Agriculture

  NSF · $50k · 2017–2019

Frequent coauthors

• Manuel E. Hernandez

  University of Illinois Urbana-Champaign

  20 shared

• Konstantinos Spiliopoulos

  19 shared

• Kay Giesecke

  Stanford University

  17 shared

• Rachneet Kaur

  16 shared

• N. Sri Namachchivaya

  University of Waterloo

  10 shared

• Armand M. Makowski

  7 shared

• James Robert Brašić

  New York City Health and Hospitals Corporation

  7 shared

• Justin Sirignano

  University of Oxford

  6 shared

Education

• M.D.

  Carle Illinois College of Medicine