| 27 May 2026
Technical Note: The Enhanced Controlled Random Search (CRS) Algorithm for Thermal History Analysis in HeFTy
Abstract. The thermal history modeling software HeFTy is one of several widely used tools for the numerical analysis of low-temperature thermochronologic data. HeFTy version 2 includes a new optional Controlled Random Search (CRS) strategy for posing the candidate time-temperature (tT) paths that are tested against data. Unlike the Monte Carlo (MC) strategy that is the default algorithm, the CRS procedure attempts to converge toward a solution. In order to overcome known limitations of CRS convergence (e.g., returning an artificially narrow range of tT solutions that exaggerates the capacity of the data to document a specific thermal history), this ‘enhanced’ CRS randomizes, expands, and reconverges on candidate tT-paths. Here, we use both synthetic and real apatite and zircon (U-Th)/He data, previously analysed using the MC algorithm in HeFTy, to explore the utility of this new tool. Overall, we demonstrate that the enhanced CRS can substantially improve computation time and is useful for finding families of tT paths that fit thermochronologic data. However, users should still expect the CRS to produce an uneven distribution of paths (i.e., ‘clustering’) in the permissible tT space. Therefore, we suggest that systematically performing multiple CRS and/or MC inversions is essential for building a robust assessment of how CRS inversion results are produced by the data and inversion design choices, or else it may not be clear what features of a CRS result are produced by the convergence algorithm rather than the data and a sample’s geologic context. Diagnosing such behaviors is essential for using thermal history inversion results for geological interpretations.
Competing interests: KM and ALSG are co-coordinators (but not associate editors) for the special issue to which this paper belongs. Otherwise, the authors declare that they have no conflict of interest.
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This technical note explores the limitations, biases, and advantages of the thermal history modeling software, HeFTy 2, with a special focus on the difference between the two underpinning algorithmic approaches, namely Monte Carlo (MC) and Controlled Random Search (CRS). The authors break down the logic and computational steps of the CRS approach in a way that is both succinct and easily digestible, which is critical to any researcher who is trying to decide which algorithm to use on their own data. The real utility of this note is that it provides guardrails for researchers to use the new CRS algorithm in HeFTY 2, which has substantially faster computing times than the MC algorithm, while remaining aware of how CRS might bias the results to show a limited range of possible time-Temperature paths. By providing clear evidence of the difference in computational labor (total runs), number of Good-Fit paths found, and clustering of results using MC and CRS approaches the authors create the framework needed to develop the most efficient modeling approach to get the largest number of possible solutions while reducing overall modeling time. I do appreciate that the authors make a point to state that though they have provided a framework for identifying biases within results from MC and CRS derived models, there is no substitute for hands on modeling when it comes to mastering the identification of biases within your own results and understanding the workings of HeFTy 2.
In addition to providing HeFTy specific modeling information, this technical note has created a platform around which discussion can be generated on “best practice” for thermal history modeling methods. Though one could argue that the results presented in this technical note would invariably have been worked out in piece-meal by any competent researcher over time, there is a tendency within the thermochronology community to interrogate the biases within a given thermal history modeling software only within the confines of their own lab group and become rigid in their modeling approach. In documenting these results and presenting them in a clear manner, the authors have saved many researchers from having to develop these HeFTy bias tests themselves and have hopefully opened up a public forum in which to debate methodology across lab groups and philosophies.
Though I do not see a need for any major revisions, I have provided a few comments on the attached PDF that would allow this note to be more easily utilized by novice modelers in developing their own HeFTy thermal histories.