Thermal tomography is a method for recovering heterogeneous thermal properties employing only boundary measurements. This paper focuses on the development of efficient inverse solvers for scenarios where the evolution of boundary conditions can vary in time. A transient heat model with two material parameters – volumetric capacity and a coefficient of thermal conductivity – is introduced for the description of the underlying physical phenomena. All proposed identification algorithms are deterministic methods based on a regularised Gauss-Newton method. A basic framework, implementation details, and the modification of general constraints initially derived for a standard setup of the Calderón problem are discussed here. Moreover, the algorithms are numerically verified for numerous examples, and results obtained show that the inverse problem exhibits a certain degree of ambiguity for a particular measurement-loading scenario. In other words, the important material property minimising the magnitude of error of the objective function seems to be the effusivity field rather than accurate identification of the individual thermal fields.

热断层扫描是一种仅使用边界测量来恢复异质热特性的方法。本文侧重于为边界条件的演变可能随时间变化的场景开发高效的逆求解器。引入了具有两个材料参数（体积容量和导热系数）的瞬态热模型来描述潜在的物理现象。所有提出的识别算法都是基于正则化高斯-牛顿法的确定性方法。此处讨论了基本框架、实现细节以及最初为 Calderón 问题的标准设置导出的一般约束的修改。此外，这些算法经过了大量示例的数值验证，获得的结果表明，逆问题对于特定的测量加载场景表现出一定程度的模糊性。换句话说，最小化目标函数误差幅度的重要材料属性似乎是扩散场，而不是单个热场的准确识别。