2024 AIChE Annual Meeting

(735x) Inferring the Shape of an Object inside of a Draining Tank Via Bayesian Statistical Inversion

In an inverse problem of reconstruction, we wish to predict the input to a physical system that produced some measured output—i.e., predict the cause of an observed effect. Bayesian statistical inversion is an approach to inverse problems that allows us to (i) incorporate prior information about the input into the solution and (ii) quantify uncertainty about the unknown input.

We tackle the following reconstruction problem with Bayesian statistical inversion. We possess an opaque, open-top tank with known geometry. A heavy, solid object is inside the tank whose geometry is unknown. To gather information about the geometry of this object via a “liquid level scan”, we fill the tank with liquid then drill a hole in its side, allowing the liquid to drain autonomously. From measurements of the liquid level in the tank over time, we wish to infer the shape of the object inside the tank—its area as a function of height. We employ Bayesian statistical inversion so we can (i) mitigate spurious “choppiness” in the inferred area function, caused by measurement noise, by imposing a smoothness prior and (ii) quantify uncertainty about the shape of the object inside the tank.