Inverse Heat Transfer Problem Research Articles

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

Accurate Temperature Reconstruction in Radiofrequency Ablation for Atherosclerotic Plaques Based on Inverse Heat Transfer Analysis.

Radio frequency ablation has emerged as a widely accepted treatment for atherosclerotic plaques. However, monitoring the temperature field distribution in the blood vessel wall during this procedure presents challenges. This limitation increases the risk of endothelial cell damage and inflammatory responses, potentially leading to lumen restenosis. The aim of this study is to accurately reconstruct the transient temperature distribution by solving a stochastic heat transfer model with uncertain parameters using an inverse heat transfer algorithm and temperature measurement data. The nonlinear least squares optimization method, Levenberg-Marquardt (LM), was employed to solve the inverse heat transfer problem for parameter estimation. Then, to improve the convergence of the algorithm and reduce the computational resources, a method of parameter sensitivity analysis was proposed to select parameters mainly affecting the temperature field. Furthermore, the robustness and accuracy of the algorithm were verified by introducing random noise to the temperature measurements. Despite the high level of temperature measurement noise (ξ = 5%) and larger initial guess deviation, the parameter estimation results remained closely aligned with the actual values, with an overall ERMS consistently below 0.05. The absolute errors between the reconstruction temperature at the measurement points TC1, TC2, and TC3, and the actual temperature, remained within 0.33 °C, 2.4 °C, and 1.17 °C, respectively. The Levenberg-Marquardt algorithm employed in this study proficiently tackled the ill-posed issue of inversion process and obtained a strong consistency between the reconstructed temperature the actual temperature.

A fast Bayesian parallel solution framework for large-scale parameter estimation of 3D inverse heat transfer problems

The inverse heat transfer problems (IHTP) have a wide range of applications in the engineering field. Bayesian methods using Markov Chain Monte Carlo (MCMC) have long been considered as a robust and effective method for solving inverse problems. However, the discretization of the problem domain by the spatio-temporal Galerkin skill, i.e., the finite element interpolation also includes the time dimension, making the scale of the unknown parameters extremely difficult for Bayesian calculations. In this paper, a fast Bayesian parallel sampling (FBPS) framework is proposed for large-scale parameter estimation of benchmark three-dimensional inverse heat transfer problems (3D-IHTP). The FBPS we developed achieves a parameter computation scale of 105 magnitude within minutes, through dimensionality reduction of the space-time dependent problem domain. The Hamiltonian Monte Carlo (HMC) sampler, which is proven to be more efficient for high-dimensional parameter estimation, is employed. Through several simulation tests of IHTP, it was confirmed that the solving efficiency of FBPS surpasses that of the traditional Bayesian strategy significantly. Finally, FBPS is successfully developed to estimate the unknown heat flux on the chip heat sink and pack interface effectively, given some simulated high resolution measurement data. The reliability and efficiency show that FBPS has the potential to support efficient prediction techniques for a class of IHTPs in engineering applications.

Application of the adaptive method to determine the process noise in the extended Kalman filter to estimate the parameters of the two dimensional inverse heat transfer problem

To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient.

A new stacking model method to solve an inverse flow and heat coupling problem for aero-engine turbine blades

The whole temperature distribution of a turbine blade is an important information for heat transfer design for turbine, but it is very difficult and expensive to measure the whole temperature filed, especially for the internal points of a blade. It is necessary to reconstruct the whole temperature distribution by calculating reversely unknown parameters based on sparse temperature values on the blade surface. This paper proposes a new stacking model method for solving inverse heat transfer problems of boundary conditions and it can be applied to cope with multi-input and multi-output regression problems. In order to improve the prediction performance of the stacking model, the Random Forest Regression, the XGBoost Regression and the K-Nearest Neighbors Regression are selected as the base estimators, and the Linear Regression is selected as the meta estimator. An application example for an aero-engine turbine blade is modeled and solved, in which the boundary condition parameters of the exhaust flows are reversely calculated and temperature distributions of a turbine blade surface can be obtained. Numerical experiments have demonstrated that the stacking model outperforms individual base models. This research is of considerable significance to heat transfer design, experimental research and decision support for real-time remote monitoring of aero-engines.

Soft computing methods in the solution of an inverse heat transfer problem with phase change: A comparative study

Inverse heat transfer problems are ill-posed problems and their solution is challenging. Conventional (hard computing) solution methods were developed for this purpose in the past, but they are not well applicable in cases including phase change, which contain strong non-linearity and bring additional computational difficulties. Soft computing methods, which currently experience very rapid development, are a promising tool for the solution of such problems. This paper addresses an inverse heat transfer problem with phase change, in which the boundary heat flux is estimated. Four methods based on distinct mathematical principles are applied to this problem and thoroughly compared. These methods include a conventional Levenberg–Marquardt method (LMM), a predictive fuzzy logic (PFL)-based method, a population-based meta-heuristic method called LSHADE (a state-of-the-art differential evolution variant), and a recently developed surrogate-assisted method coupled with differential evolution, referred to as LSADE method. Furthermore, a reformulation of the problem was developed, utilising a dimension reduction scheme and a decomposition scheme that led to sub-problems with different time frames. This reformulation brought extensive computational improvements. Results of the comparison of the methods then showed that the LMM and the PFL behave well in case without phase change but their performance deteriorates substantially in case with phase change. The LSHADE and the LSADE showed superior performance in the solution of the inverse problem with the phase change. Moreover, their performance was rather stable and insensitive to the location of the temperature sensor, which was the source of data for the estimation.

Thermal relaxation parameters estimation of non-Fourier heat transfer in laser-irradiated living tissue using the Levenberg-Marquardt algorithm

The present work is concerned with solving the inverse heat transfer problem (IHTP) to estimate the thermal relaxation parameters corresponding to the dual phase lag (DPL) model-based bio-heat transfer in laser-irradiated living tissue. This problem is divided into two parts: direct and inverse problems. The solution of the inverse problem has been obtained using the Levenberg–Marquardt algorithm. On the other hand, the solution to the direct problem is obtained by solving the DPL model-based bio-heat transfer equation (BHTE) with the transient radiative transfer equation (TRTE). So, the TRTE has been numerically solved by the modified discrete ordinate method (DOM) to find the intensity field in the living tissue subjected to short-pulsed laser radiation, and it acts as a heat source in the DPL model-based BHTE. So, the DPL model-based BHTE has been analytically solved by employing the finite integral transform technique to get the temperature variation inside the laser-irradiated living tissue. First, the computer code developed for estimating unknown thermal relaxation parameters using the Levenberg–Marquardt algorithm has been verified against the data given in the literature, and found good agreement between them. Then, the thermal response of laser-irradiated living tissue has been investigated. After that, the influence of sensor position on the sensitivity of the IHTP solution has been discussed. The impact of the total transient readings and the measurement error on estimating the unknown parameters have been investigated. The present study’s findings can significantly contribute to various parameter estimation problems where the conventional methods for direct measurements of parameters are impossible or very difficult. Furthermore, the current results may considerably impact the study of the thermic response of living tissue during laser-based photothermal therapy.

Implementation of the inverse problem for on-chip PCR diagnostics with rapid and precise thermal cycling

Microfluidic devices have emerged as a promising platform for point-of-care biological analysis, including PCR-based molecular diagnostics. However, the multi-layer characteristics of existing microfluidic chips introduce significant thermal inertia, resulting in temperature disparities between the PCR mixture and the heating element. This issue poses a substantial obstacle to the efficient and accurate deployment of point-of-care technology. Herein, a practical approach for accurate and fast PCR on microchips based on the inverse heat transfer problem (IHTP) is introduced and solved by incorporating computational fluid dynamics (CFD) simulations and the particle swarm optimization (PSO) algorithm. The methodology successfully resulted in a 46% reduction in PCR duration with less than 0.1 ℃ temperature discrepancy for our custom-built microfluidic device. The optimization performance was further evaluated by conducting biological tests at varying concentrations of the genetic sequence, and the standard curve of our optimized PCR system is presented. According to the standard curve of the system, using an optimized boundary temperature profile, the fabricated benchtop testing device performed COVID-19 molecular detection with 104% efficiency. The numerical approach can be extended to a variety of microfluidic devices and PCR temperature protocols, thereby enhancing the PCR diagnosis in microfluidic devices.

Автоматизация расчета реактора для синтеза серосодержащего сорбента, предназначенного для извлечения из сточных вод ионов тяжелых металлов

An automated algorithm for calculating the time of the full cycle of operation, the stages of thermal stabilization and cooling of the reaction mixture in a reactor designed for the synthesis of a sulfur-containing sorbent produced on the basis of waste products from metallurgy, petrochemistry (sulfur), epichlorohydrin (1, 2, 4-trichloropropane) and the pulp and paper industry (lignin) for extraction from wastewater of heavy metal ions. The use of algorithms and a program for automated calculation of the reactor helps to reduce the complexity of production costs and the cost of the finished sorbent, increases the reliability of calculations and the quality of design solutions. The developed algorithms and program include the following calculation routines: physico-chemical properties of the components of the reaction mixture and the choice of a mixing device (propeller three-bladed agitator), taking into account the viscosity of the mixture; hydrodynamic calculation of the mixing device and heat transfer when heating the mixture from 20 to 45 °C; heat transfer during thermal stabilization and cooling of the working mixture, as well as the time of the full cycle of the reactor. The proposed algorithm of heat transfer during thermal stabilization of the reaction mass is based on the determination of the temperature range of water heating, compensating for heat losses. For this purpose, the inverse problem of heat transfer with unknown temperatures over a hot heat carrier is formulated and solved, such that the average value between them is a thermostabilizable value. An algorithm for calculating the cooling process of the reaction mixture in a sulfur-containing sorbent synthesis reactor, taking into account heat losses to the environment in the amount of 5%, is presented. A program has been developed that implements the presented algorithms in C#, designed to automate the calculation of a sulfur-containing sorbent synthesis reactor designed to extract heavy metal ions from wastewater.

The reduction of ill-posedness of the inverse heat transfer problem in rotating disc cavities using the wall temperature characteristics as the priori knowledge

Solving the heat conduction equation using surface measurement temperature as boundary conditions to obtain surface heat flux is an ill-posed inverse heat transfer problem, in which small temperature errors can create large uncertainties in heat flux. This paper proposes a RBF (Radial Basis Function) + BP (Back Propagation) neural network approximation method that uses the wall temperature characteristics as priori knowledge to reduce the ill-posedness of the inverse heat transfer problem in rotating disc cavities of aero-engines. The wall temperature characteristics are described using first-order derivative, which are discussed and obtained through analytical solution and fluid-thermal coupling numerical simulation. Bayesian inference theory is used to construct neural network training objective function with regularization term and the RBF + BP neural network approximation method with uncertain regularization coefficient is proposed. Numerical experiments were conducted based on numerical simulation data to verify the effectiveness of the proposed method. The results show that the method can effectively suppress the ill-posed nature of the inverse heat transfer problem and can reduce the heat flux relative error level by 1 ∼ 2 orders of magnitude compared with several traditional data fitting methods commonly used in rotating disc cavities. The method of densifying measurement points combined with priori knowledge revision near the air impact point can effectively capture the local heat flux characteristics caused by airflow impact. The RBF + BP approximation method can reduce the demand for measurement points by approximately 44 ∼ 60 % under the error of 3σ = 0 K ∼ 0.9 K compared with Bayesian inference method.

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

Fuzzy Levenberg-Marquardt damping factor update strategy and Tikhonov regularization applied to a coupled conduction-radiation inverse heat transfer problem

The recently proposed Fuzzy Levenberg-Marquardt Damping Factor Updating Strategy (FLM) is used along with Tikhonov Regularization (TR) in order to solve a coupled conduction-radiation function estimation inverse problem. FLM consists of updating the Levenberg-Marquardt (LM) damping factor with the assist of Fuzzy Logic. To test the FLM algorithm combined with TR, a conduction-radiation problem is addressed, and it serves as test bed to the numerical experiments, where the objective is to obtain estimatives of parameters, such as the spatially variable scattering albedo, the thermal conductivity and the optical thickness, simultaneously, which is often performed separately. Two main test cases are presented, one considering only the radiation problem, used as benchmark, in order to investigate noise levels and hyperparameters. The second main test case deals with the coupled conduction-radiation heat transfer problem for different functional forms of the spatially variable scattering albedo. For all presented numerical experiments, good estimates were achieved for the sought functions and parameters. These results demonstrate that the methodology presented in this work, through the combination of the Fuzzy LM dampting factor updating strategy and the Tikhonov regularization scheme, may provide valuable tools for inverse heat transfer problems.

An inverse problem to estimate simultaneously the heat source strength for multiple integrated circuit chips on a printed circuit board

<abstract> <p>In this three-dimensional steady-state inverse heat transfer problem, we determine the magnitude of the spatially dependent volumetric heat source originating from multiple encapsulated chips mounted on a printed circuit board (PCB). Prior to the estimations, the functional form of the multiple heat sources is treated as unknown, leading to its classification as a function estimation challenge within the realm of inverse problems. The utilization of the conjugate gradient method (CGM) as an optimization tool is rooted in its distinct advantage of not requiring any a priori knowledge regarding the functional form of the unidentified quantities. Furthermore, the CGM empowers the simultaneous correction and estimation of multiple unknowns during each iteration, thereby ensuring the consistent possibility of precise estimates.</p> <p>To affirm the precision of the estimated heat source attributed to multiple chips, a series of numerical experiments were conducted. These experiments encompassed varying inlet air velocities and introduced measurement errors. Notably, the results revealed that meticulous measurements consistently yielded accurate heat generation assessments for the chips, regardless of the prevailing air velocity conditions. The findings underscored that the accuracy of chip heat generation estimates diminished as measurement errors escalated, predominantly due to the ill-posed nature inherent in the inverse problem.</p> </abstract>

Analysis of Cavity Disk Heat Transfer by Solving Inverse Heat Transfer Problem

Abstract The flow and heat transfer within compressor rotor cavities of aero-engines is a conjugate problem. The operating conditions buoyancy forces, caused by radial temperature difference between the cold throughflow and the hotter shroud, can influence the amount of entrained air significantly. By this, the heat transfer depends on the radial temperature gradient of the cavity walls, and in turn, the disk temperatures are dependent on the heat transfer. In this article, disk Nusselt numbers are calculated in reference to the air inlet temperature and in comparison to a modeled local air temperature inside the cavity. The local disk heat flux is determined from measured steady-state surface temperatures by solving the inverse heat transfer problem in an iterative procedure. The conduction equation is solved on a 2D mesh using a validated finite element approach, and the heat flux confidence intervals are calculated with a stratified Monte Carlo approach. An estimate for the amount of air entering into the cavity is calculated by a simplified heat balance. The major influences on the Nusselt number were found to be the mass flowrate entering the cavity and the density of the fluid inside the cavity.

A Neural Network-Based Method for Real-Time Inversion of Nonlinear Heat Transfer Problems

Inverse heat transfer problems are important in numerous scientific research and engineering applications. This paper proposes a network-based method utilizing the nonlinear autoregressive with exogenous inputs (NARX) neural network, which can achieve real-time identification of thermal boundary conditions for nonlinear transient heat transfer processes. With the introduction of the NARX neural network, the proposed method offers two key advantages: (1) The proposed method can obtain inversion results using only surface temperature time series. (2) The heat flux can be estimated even when the state equation of the system is unknown. The NARX neural network is trained using the Bayesian regularization algorithm with a dataset comprising exact surface temperature and heat flux data. The neural network takes current and historical surface temperature measurements as inputs to calculate the heat flux at the current time. The capability of the NARX method has been verified through numerical simulation experiments. Experimental results demonstrate that the NARX method has high precision, strong noise resistance, and broad applicability. The composition of the input data, the surface temperature measurement noise, and the boundary heat flux shape have been studied in detail for their impact on the inversion results. The NARX method is a highly competitive solution to inverse heat transfer problems.

Applying multivariate inverse heat conduction problem to determine thermal contact resistance in aircraft embedded systems

In the field of heat transfer, inverse problems deal with the estimation of parameters that are difficult to measure directly. The usefulness of inverse techniques is such that, due to severe conditions, direct measurement of a certain variable becomes inaccessible. This works aims to perform inverse estimation in two problems. The first case is related to the estimation of the heat flux boundary condition and thermal contact resistance between two SAE 1020 steel plates. The first case is used as validation for the second case and is solved using the finite volume method for the discretization of the diffusion equation and Successive Over Relaxation (SOR) for solving the system of linear eqs. A set of seven one-dimensional experiments were performed varying the roughness and contact pressure at the interface of the samples and, as expected, it was found that the thermal conductance is a function of these parameters. The second case consists in the estimation of three thermal resistances in an aircraft embedded system consisting of four components and ambient air. In this case, the direct problem is solved using fourth-order Runge-Kutta to solve the system of ODEs. In both cases a future times regularization technique approach combined with Markov Chain Monte Carlo (MCMC) optimization method is used to solve the inverse problem. The embedded system inverse problem is also solved using a new and simple approach based on the Quadrilateral Optimization Method (QOM) with future time steps regularization and the result is compared with the MCMC method. The results of this work consolidate a low-cost inverse estimation setup and attest to the capacity of multivariate estimation in inverse heat transfer problems.

Experimental evaluation and quantitative modeling of thermal behavior of surface-attached insulation polymers and steel structures under combustion

The surfaces of liquefied petroleum gas (LPG) storage vessels are usually coated with polymer insulation to maintain low temperatures. However, this insulation layer poses a potential fire risk. This study aimed to investigate the heat feedback mechanism and its impact on steel structures when bonded thermal insulation materials combust. Thermal insulation materials were bonded to Q345 steel surface, which is commonly used in LPG storage tanks, and experiments were conducted by designing a burning experimental rig of the combustible material attached to steel plate. Results revealed the existence of an equivalent temperature layer in the flame zone above the insulation material. Equations for predicting radiative and convective heat feedback were formulated. As combustion of the insulation material stabilized, the predicted heat feedback from the equations closely matched experimental values. A quantitative evaluation method, based on the inverse heat transfer problem, was proposed. This method determines the thermal decay function of heat feedback through the insulation material and steel plate. By establishing three key performance indicators, this work achieved independent quantification of potential thermal concerns and robustness evaluations of steel structures with surface-bonded insulation materials under combustion.

A review of regularization strategies and solution techniques for ill-posed inverse problems, with application to inverse heat transfer problems

With the presence of a large number of inversion algorithms for inverse heat transfer problems (IHTPs) and non-IHTPs, a need for review to have a holistic view is seen. An exhaustive literature review, with the motivation of selecting the inversion technique best fit for a given problem, was made for a general inverse problem. For ill-posedness, a classification of available regularization algorithms namely Tikhonov’s regularization, Bayesian regularization, mollification method, Beck’s sequential approach and Alifanov’s iterative approach, has been provided. Inversion methods like singular value decomposition, truncated singular value decomposition, Tikhonov regularization and total variation regularization are explained. Optimization methods namely steepest descent method, conjugate gradient method, Newton method, Levenberg–Marquardt method, Lagrange method, adjoint method, function specification method, genetic algorithm, differential evolution and particle swarm optimization (PSO) are reviewed. Further, a technique based on neural networks is studied, and wavelet methods like shrinking and wavelet vaguelette decomposition are reviewed. Associated literature has also been listed, highlighting the gaps. The usability of various algorithms in IHTP, starting from the golden section search method, for retrieval of a single parameter, to the regularized versions of the inversion technique, for retrieval of multiple parameters with uncertainty, demonstrates real-life applications to fins in IHTP. An inversion algorithm capable to handle every kind of nonlinearity is sought in literature, whose absence raises the research question, “Is there a technique that works globally for every inverse problem?”, is asked prior to, “What if the available techniques were not utilized to an extent that they should?” is posed. In lieu of this gap, a general comparative framework is developed, such that an efficient technique is selected, based on the total minimum error, which can be used in any field of interest.

Estimation of soils thermophysical characteristics in a nonlinear inverse heat transfer problem

It is well known that knowledge of thermophysical parameters is a leading strategy to research effects of energy transfer in soils. The present article proposes an inverse analysis for numerical solving of nonlinear heat transfer problem to determine the thermophysical properties of two different soil types: sand and chernozem. First, estimation of thermophysical parameters is performed using temperature data from experimental set-up, which is two-chambered container for two soil types. Second, numerical algorithm is based on implicit Euler scheme for discretization, Newton method to solve nonlinear system of equations and Levenberg-Marquardt method to minimize nonlinear estimator with Tikhonov's regularization technique. Simulations have been efficiently carried out for two different soil types, showing that the reliability of the model is satisfying with a discrepancy between numerical predictions and experimental observations remaining within the measurement error.

Physics-informed learning for thermophysical field reconstruction and parameter measurement in a nano-porous insulator's heat transfer problem

To deeply explore aerogel's insulation performance, we proposed a thermophysical field reconstruction based on physics-informed learning with limited parameters measurement. It's the first time that the model has been utilized to make high-precision measurements of thermophysical parameters in heat transfer problem. In this work, the monolithic aerogel's center temperature response is measured, and the thermal conductivity is extracted at small (< 15 K), medium and large (≥ 400 K) temperature differences, respectively. By leveraging the physics-informed learning method, the temperature field can be reconstructed and thermophysical parameters are precisely identified collaboratively, yielding the majority error within 5% and 1%, respectively. Additionally, our method solves the inverse problem of nonlinear heat transfer. The heat conduction and the overall transport attenuation coefficient of thermal radiation are precisely identified at large temperature differences (≥ 400 K), and the majority of errors are <2% and 4%, respectively. Moreover, the opacifier-doped aerogel displays the lowest thermal radiation contribution of 6.36% at temperature differences (≈ 700 K), whereas pure aerogel shows the highest contribution of 35.40%. Notably, the temperature field exhibits significant nonlinearity currently. The proposed study of experiments and model provides a novelty method to make high-precision measurements, which make up the gap of the classical numerical methods.