Beyond best-fit: a new approach to thermal analysis

Understanding how heat is generated and exchanged in materials is crucial to many engineering applications, including additive manufacturing and microchip design. In traditional measurement approaches for thermal transport, scientists often use a “best-fit” approach to estimate a single value for a property of interest.

This method assumes that all other secondary variables describing the sample being measured, such as the thickness of a material layer, or the way that energy is being deposited, are perfectly known. If these assumptions are slightly off, the prediction can be misleadingly precise, or suggest a distinctly different value. To address these issues, members of Rachel Kurchin and Jonathan Malen’s research groups worked on applying Bayesian Parameter Estimation (BPE) to analysis of an experiment that typically relies on other techniques.

Recently published work from team members spanning materials science and engineering and mechanical engineering explores BPE as a more robust way to analyze how heat moves through materials, applying the method to Frequency-Domain Thermoreflectance (FDTR), which uses lasers to measure material properties such as thermal conductivity and interface conductance.

Instead of producing a single "best" number, BPE generates a probability distribution, offering a visual that indicates every plausible value for a property and the likelihood of each. BPE can also reflect when there is low confidence in the data fit and signal when background assumptions may be incorrect.

 “Using BPE offers a lot of desirable things that you would look for in an inference,” said J. Drew, a doctoral candidate in research professor Kurchin’s research group. “We use it as an uncertainty quantification proxy, and it can evaluate multiple parameters simultaneously.” 

In this study, the researchers looked at a sample analysis based on the thermal conductance of a gold/sapphire interface. They made an assumption of the gold transducer layer’s thickness, based on the deposition machine's settings. However, when they ran the BPE analysis, the model consistently indicated that the data more closely matched the behavior of a thicker gold layer. Guided by this output, the team performed measurements and determined that the gold was actually notably thicker than initially assumed, well outside the typical variation due to the roughness of the surface. This, in turn, was changing the predicted thermal response of the material. By correcting this single assumption, they were able to draw more accurate conclusions about the material’s thermal properties.

Using Bayesian Parameter Estimation offers a lot of desirable things that you would look for in an inference

J. Drew, Doctoral candidate, CMU Materials Science & Engineering

The researchers have made the computational code publicly available, hoping that other labs that study thermal transport will adopt this framework as it can provide a higher level of interpretability and confidence. 

Kurchin’s group had previously applied BPE to analysis of solar cell measurements, and this work was the first exploration of using it to analyze other materials systems. 

“It was interesting for us to learn more about these thermal transport techniques and how BPE could be helpful in a totally different community,” Kurchin remarked. “The reviewers of the manuscript called it a ‘seminal paper,’ which speaks to the amazing work that the whole team put in.”