We provide a tutorial on the Bayesian statistical approach to inverse problems. Two categories of inverse problems are: (1) infer parameters in a model of a system from observations of input-output pairs and (2) reconstruct the input to a system that caused an observed output. Bayesian statistical inversion (BSI) provides a solution to inverse problems that (i) quantifies uncertainty by assigning a probability to each region of parameter/input space and (ii) allows for incorporation of prior information/beliefs about the parameters/inputs. We demonstrate BSI on problems pertaining to heat transfer into a lime fruit; eg. reconstruct the initial temperature of a lime from a measurement of its temperature later in time.
[Joint work with: Faaiq Waqar and Swati Patel at Oregon State University.]
Cory Simon is an assistant professor of chemical engineering at Oregon State University. He earned his PhD in Chemical Engineering from the University of California, Berkeley. His research group develops mathematical models, trains machine learning models, and conducts computer simulations to tackle or deliver insights into problems in chemistry and materials science.