This paper aims to noninvasively estimate the sizes and locations of tumors via the surface temperature in the skin tissue. The famous 2D Pennes bioheat transfer equation is used to describe the heat transfer behavior in the skin tissue, which is solved by the recently-developed meshless generalized finite difference method (GFDM) in the proposed solver. The hybrid optimization algorithm based on genetic algorithm (GA) and Levenberg–Marquardt algorithm (LM) is introduced to estimate the sizes and locations of tumors. The efficiency of the proposed GA–LM–GFDM solver is verified under several benchmark examples. Numerical investigation shows that the tumor characteristics can still be accurately estimated with the contaminated temperature data measured on the skin surface.

In the development of the prediction model for soil liquefaction, compared to the stress-based method, the energy-based methods proposed and developed in recent years are closer to the essence of soil liquefaction which is about the energy dissipation. Therefore, considering the weak nonlinear relationship found by the previous research, the fuzzy neural network (FNN) and BP neural network (BPNN) were adopted to try to obtain a prediction model which is the most proper to this nonlinear relationship. Firstly, the database including 284 cases obtained from laboratory test was divided into three separate groups denoted as training, validation set and testing sets by the ratio of 5:1:1; then, the FNN model and BPNN model were iterated to determine the model parameter by referring to the variation of fitness value and relative error of validation set; at the same time, the optimization algorithm of genetic algorithm (GA) was adopted to BPNN to find the best coefficients; besides, the parameter of 𝐶 𝑐 and 𝐷 50 was respectively excluded from the database to test their influence degree according to the prediction error; finally, 6 prediction results of FNN and genetic algorithm BP neural network (GABP) were compared with the previously proposed models. The results showed that the relationship of capacity energy to the influencing parameters could not be fitted as a fully linear relationship; the FNN model can learn the role of 𝐶 𝑐 in affecting the capacity energy while the GABP model needs not to take it into account; the FNN and GABP model all fitted 2 a good weakly nonlinear relationship for the capacity energy, and the GABP model is a better prediction model for capacity energy so far.

In the development of the prediction model for soil liquefaction, compared to the stress-based method, the energy-based methods proposed and developed in recent years are closer to the essence of soil liquefaction which is about the energy dissipation. Therefore, considering the weak nonlinear relationship found by the previous research, the fuzzy neural network (FNN) and BP neural network (BPNN) were adopted to try to obtain a prediction model which is the most proper to this nonlinear relationship. Firstly, the database including 284 cases obtained from laboratory test was divided into three separate groups denoted as training, validation set and testing sets by the ratio of 5:1:1; then, the FNN model and BPNN model were iterated to determine the model parameter by referring to the variation of fitness value and relative error of validation set; at the same time, the optimization algorithm of genetic algorithm (GA) was adopted to BPNN to find the best coefficients; besides, the parameter of \({C}_{c}\) and \({D}_{50}\) was respectively excluded from the database to test their influence degree according to the prediction error; finally, 6 prediction results of FNN and genetic algorithm BP neural network (GABP) were compared with the previously proposed models. The results showed that the relationship of capacity energy to the influencing parameters could not be fitted as a fully linear relationship; the FNN model can learn the role of \({C}_{c}\) in affecting the capacity energy while the GABP model needs not to take it into account; the FNN and GABP model all fitted a good weakly nonlinear relationship for the capacity energy, and the GABP model is a better prediction model for capacity energy so far.