A tutorial on the Bayesian statistical approach to inverse problems
Inverse problems are ubiquitous in science and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input–output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2023-12-01
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| Series: | APL Machine Learning |
| Online Access: | http://dx.doi.org/10.1063/5.0154773 |
| _version_ | 1827391479896604672 |
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| author | Faaiq G. Waqar Swati Patel Cory M. Simon |
| author_facet | Faaiq G. Waqar Swati Patel Cory M. Simon |
| author_sort | Faaiq G. Waqar |
| collection | DOAJ |
| description | Inverse problems are ubiquitous in science and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input–output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a “solution” that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our Tutorial aims to reach a wide range of scientists and engineers. |
| first_indexed | 2024-03-08T17:11:35Z |
| format | Article |
| id | doaj.art-28f3a57d33d24629b1bdb86db8776bc7 |
| institution | Directory Open Access Journal |
| issn | 2770-9019 |
| language | English |
| last_indexed | 2024-03-08T17:11:35Z |
| publishDate | 2023-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Machine Learning |
| spelling | doaj.art-28f3a57d33d24629b1bdb86db8776bc72024-01-03T19:54:29ZengAIP Publishing LLCAPL Machine Learning2770-90192023-12-0114041101041101-2010.1063/5.0154773A tutorial on the Bayesian statistical approach to inverse problemsFaaiq G. Waqar0Swati Patel1Cory M. Simon2School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon 97331, USADepartment of Mathematics, Oregon State University, Corvallis, Oregon 97331, USASchool of Chemical, Biological, and Environmental Engineering, Oregon State University, Corvallis, Oregon 97331, USAInverse problems are ubiquitous in science and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input–output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a “solution” that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our Tutorial aims to reach a wide range of scientists and engineers.http://dx.doi.org/10.1063/5.0154773 |
| spellingShingle | Faaiq G. Waqar Swati Patel Cory M. Simon A tutorial on the Bayesian statistical approach to inverse problems APL Machine Learning |
| title | A tutorial on the Bayesian statistical approach to inverse problems |
| title_full | A tutorial on the Bayesian statistical approach to inverse problems |
| title_fullStr | A tutorial on the Bayesian statistical approach to inverse problems |
| title_full_unstemmed | A tutorial on the Bayesian statistical approach to inverse problems |
| title_short | A tutorial on the Bayesian statistical approach to inverse problems |
| title_sort | tutorial on the bayesian statistical approach to inverse problems |
| url | http://dx.doi.org/10.1063/5.0154773 |
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