In this work, we examine the application of open-loop non-linear model predictive control (NMPC) to a specific partial differential equation (PDE) reaction-diffusion system. Instead of attempting to stabilize a particular state, we focus only on reaching the desired state at a given time. This problem is motivated by applications to in-vitro synthesis of tissues whose formation is governed by reaction-diffusion models. The PDE model is discretized into a finite set of nonlinear ordinary differential equations using finite-elements, after which a NMPC algorithm is used to derive the desired control actions. Results for one- and two- dimensional systems demonstrate the feasibility of the approach, but also highlight a dependency on the number of actuators and computational power.
Clinicians, policymakers, psychologists, and economists often ask causal questions: does this treatment or intervention cause the observed differences in outcome? If researchers can observe both outcomes under treatment (intervention or exposure) and control for each unit, then researchers can directly measure the causal effect. However, the inability to observe both outcomes forms the fundamental problem of causal inference. Answers to these questions require formal frameworks to interpret statistical quantity with causality. While the gold standard of causality stems from randomized controlled trials or experiments due to treatment assignment randomization, observational studies are increasingly popular for researchers to discover existing phenomena and surveillance to provide real-world evidence. Covariates, measured alongside treatment and outcome, are used in modern causal inference to improve analyses in observational and experimental studies. This dissertation proposes methods to thoughtfully identify and adjust for covariates in observational study design, risk factor analysis, and randomized trial analysis. In Chapter 2, we advocate for a new visualization tool, the joint variable importance plot, to help researchers prioritize confounders for adjustment in observational study design. In Chapter 3, we present variable importance from prediction and as-if causal perspective to evaluate mortality risk factors. Lastly, we encourage practitioners to adopt prognostic covariate adjustment with efficient estimators when analyzing small randomized trials in Chapter 4.
Cookie SettingseScholarship uses cookies to ensure you have the best experience on our website. You can manage which cookies you want us to use.Our Privacy Statement includes more details on the cookies we use and how we protect your privacy.
