# Bayesian inference of the area profile of a solid in a draining tank using Turing.jl

**URL:** <https://discourse.julialang.org/t/bayesian-inference-of-the-area-profile-of-a-solid-in-a-draining-tank-using-turing-jl/126995>\
**Category:** Probabilistic Programming\
**Created:** [March 15, 2025, 11:32pm UTC](https://discourse.julialang.org/t/bayesian-inference-of-the-area-profile-of-a-solid-in-a-draining-tank-using-turing-jl/126995 "2025-03-15T23:32:43Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Cory\_Simon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cory_simon/32/3950_2.png) [@Cory\_Simon](https://discourse.julialang.org/u/Cory_Simon)\
**Post date:** [March 15, 2025, 11:32pm UTC](https://discourse.julialang.org/t/bayesian-inference-of-the-area-profile-of-a-solid-in-a-draining-tank-using-turing-jl/126995/1 "2025-03-15T23:32:43Z")

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👋 I am a chemical engineering professor at Oregon State University. we used Turing.jl to solve an inverse problem of reconstruction with quantified uncertainty: infer the horizontal cross-sectional area profile of a solid inside of a tank from the liquid level dynamics as the tank drains. mathematically, this comes down to Bayesian inference of a function involved in a differential equation.

thought to share with you all since  
(1) it’s a neat example of applying Bayesian inference to a physical inverse problem  
(2) as practitioners, we appreciate how easy Turing.jl was to use for this, and it enabled our research. (thank you, developers.)

> **[Inferring the cross-sectional area profile of an unseen solid in a draining...](https://www.sciencedirect.com/science/article/pii/S0009250925003112)**
>
> We aim to reconstruct the horizontal cross-sectional area profile of an exogenous, heavy, unseen solid contained in a tank from measurements of the li…

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**Author:** ![Olivier\_Merchiers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/olivier_merchiers/32/4073_2.png) [@Olivier\_Merchiers](https://discourse.julialang.org/u/Olivier_Merchiers)\
**Post date:** [March 16, 2025, 9:13am UTC](https://discourse.julialang.org/t/bayesian-inference-of-the-area-profile-of-a-solid-in-a-draining-tank-using-turing-jl/126995/2 "2025-03-16T09:13:48Z")

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Thanks for sharing!  
Very nice paper indeed. I was looking for something like this.  
Did you use Makie.jl for the figures?

Best,  
Olivier

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**Author:** ![Cory\_Simon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cory_simon/32/3950_2.png) [@Cory\_Simon](https://discourse.julialang.org/u/Cory_Simon)\
**Post date:** [March 16, 2025, 4:43pm UTC](https://discourse.julialang.org/t/bayesian-inference-of-the-area-profile-of-a-solid-in-a-draining-tank-using-turing-jl/126995/3 "2025-03-16T16:43:35Z")

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thank you! we used Makie.jl for the figures indeed. (maybe should have cited the Makie.jl paper, too.) we applied a theme from MakieThemes.jl.