Abstract: Machine learning is the study of how artificial intelligence mimics the human ability to learn. This is a gentle and interactive introduction to the types of questions involved in machine learning and some of the algorithms used to address those questions.
Abstract: In the late 1800s, Oliver Heaviside popularized a technique for solving differential equations by treating derivatives and integrals as variables. Heaviside was able to derive correct results, but did not rigorously justify his methods. In the early 1900s, many mathematicians attempted to formalize Heaviside’s work by use of integral transforms. These attempts were successful enough to make their way into many undergraduate differential equations curricula.
In this talk we consider optimal recovery of the solution to an elliptic boundary value problem. It is assumed that boundary data are unknown. Compensating information is provided in the form of a finite number of measurements of the solution, but even with this additional information solution of this problem is not unique. We will discuss an optimal recovery framework for determining a "best possible" version of the solution and define its finite element approximation.