My research interests are primarily in the fields of modeling, numerical analysis, optimization and control that are motivated by problems arising in the areas of science and engineering.

• Sep. 2021-Present Traffic Flow
  • Create variant models to simulate real energy consumption process.
  • Details see CIRCLES.
• Sep. 2018-Aug. 2021 University of Southern California Graduate Student Researcher
  
  • Conducted transdermal alcohol biosensor research funded by NIAAA and NIH.
  • Formulated a forward model based on the diffusion process of ethanol from the blood through the skin to the biosensor, and considered a real-time deconvolution problem for the diffusion equation to estimate blood alcohol concentration or breath alcohol concentration from transdermal alcohol concentration data based on a discrete-time Linear Quadratic Gaussian (LQG) tracking problem for an abstract parabolic system with random parameters.
  • Developed a discrete-time Linear Quadratic Regulator (LQR) in infinite-dimensional spaces for abstract parabolic systems with random parameters. Developed a finite-dimensional approximation and corresponding convergence theory and carried out numerical studies.
• Sep. 2018-Oct. 2018 Exploring Influential Factors for Red Wine Taste Preferences
  
  • Explored which chemical properties substantially influence the quality of red wines.
  • Analyzed the database of red wine from UCI machine learning repository by basic statistic tools such as histograms, scatterplot matrix, correlation matrix.
  • Treated wine quality as a continuous output, analyzed further by fitting different regression models using simple linear regression, Lasso regression, primary component regression and best subset selection.
  • Evaluated different models by mean square error using 10-fold cross-validation. Taking the strong correlation between evaluating the quality of red wine and personal preference into consideration, modified the formula of accuracy percentage by allowing data obtained from different models to lie within a reasonable range of true data from database.
• Sep. 2014-May. 2016 Research on the Convergence of the Inexact Semi-Proximal ADMM
  
  • Researched on classical Alternating Direction of Method of Multipliers (ADMM) and semi-proximal ADMM.
  • Proposed the first inexact algorithm by using the error bound functions. Demonstrated that the inexact algorithm can go on without solving the solutions to sub problems exactly. Moreover, proved the convergence of the method in the case of this inexactness criterion.
  • Proposed the second inexact algorithm by adding to the sub-problems a term whose module is determined by the distance between the exact solution and inexact solution, and also a correct step. Proved the convergence of the method in the case of this inexactness criterion.
• Nov. 2011-Nov. 2012 Leader in Undergraduate Innovation and Entrepreneurship Training Program
  
  • Winner of the Excellence Prize in 2011 Undergraduate Innovation and Entrepreneurship Training Program.
  • Created a new method based on wavelet transformation to solve the image blurring problems and performed programming experiments with Matlab.
  • Designed an imagine processing software GUI based on proposed method.
Publications
Talks

1. Yao, Mengsha, Luczak, Susan, and Rosen, Gary, Tracking and Blind Deconvolution of Blood Alcohol Concentration from Transdermal Alcohol Biosensor Data: A Population Model-Based LQG Approach in Hilbert Space, Automatica, Sep, 2022
2. Yao, Mengsha, Luczak, Susan, Saldich, Emily and Rosen, Gary, A Population Model-Based LQG Compensator for the Control of Intravenously-Infused Alcohol Studies and Withdrawal Symptom Prophylaxis Using Transdermal Sensing, DOI: 10.1002/oca.2934, Optimal Control Applications and Method, July, 2022
3. Yao, Mengsha, Luczak, Susan, and Rosen, Gary, Linear Quadratic Gaussian Control of Random Abstract Parabolic Systems, 60th IEEE Conference on Decision and Control (CDC), Austin, Dec, 2021
4. Yao, Mengsha, Luczak, Susan, and Rosen, Gary, Development of a Real-Time Output Feedback Controller for Alcohol Clamping Experiments Based on a Population Model for the Transdermal Transport of Alcohol, Alcoholism: Clinical and Experimental Research, Vol. 45, No. 6, June, 2021
5. Yao, Mengsha and Zhang, Liwei, Convergence of the Inexact Semi-Proximal Alternating Direction Methods of Multipliers, Master’s Thesis. Included in China Master’s Theses Full-Text Database, June, 2016

1. Yao, Mengsha, Mathematical Challenges and Opportunities for Autonomous Vehicles Reunion Conference, Lake Arrowhead, CA, June 5-10, 2022, slides
2. Yao, Mengsha, 60th IEEE Conference on Decision and Control (CDC), Dec. 15, 2021, video
3. Yao, Mengsha, Seminar Topic: LQ Control, Estimation, and Tracking for Random Abstract Parabolic Systems with Application to a Transdermal Alcohol Biosensor Estimator, TU, Sep. 29, 2021
4. Yao, Mengsha, Annual Alcohol Workshop, USC, Feb. 22, 2021, pdf