# A Systematic Compact Model Parameter Calibration with Adaptive Pattern Search Algorithm
## 5 Results  
### Adaptive Pattern Search  
#### 5.1.1 Adaptive Pattern Move  
For the pattern move defined as in the conventional HJ method, searching basis moves forward to searching direction by constant step [10; 11]. This is simple and uses no other computation, except for the evaluation of the point reached. However, it is too naive and cannot utilize the information gained spontaneously during pattern move, such as the trajectory of losses and momentum, which can assist the process in figuring out the shape of parameter space. In the case of very small magnitude of the pattern vector, it often travels in the low slope region unnecessarily and takes lots of iterations in the pattern move (Red arrows in the Figure 3a). If the magnitude of the pattern vector increases as the slope of the valley decreases, it can pass through gradual region much faster than constant pattern vector and reduce the iterations of the pattern move (Blue arrows in the Figure 3a). On the contrary, if the magnitude of pattern vector is too large to sample the loss valley properly, it just hops over the hillocks in the parameter space and misunderstands the underlying shape of the valley (Red arrows in the Figure 3b). As the rough sampling with constant pattern vector, it misjudges as it explores the gradual valley. If the magnitude of pattern vector is varied with respect to the information of the parameter space, it has a chance to fumble around and figure out the underlying geometry. In the toy model described in Figure 3b, it settles in the first valley as intended owing to the adaptive pattern move (Blue arrows in the Figure 3b). In this study, the normalized differences in fitness values between the two neighboring points is utilized in the pattern move to scale the searching step adaptively. As the patter vector advances, it is inversely scaled by the normalized difference of losses between the points. The implementation of adaptive pattern move is depicted in Figure 3c.  
Figure 3: (**a**) The graphical interpretation of pattern move when the pattern vector is relatively small and fitness valley has a gradual slope. Red arrow represents the pattern vector of the conventional method and blue arrow represents the adaptive pattern vector. Unnecessary iteration of evaluations and advances is needed with this circumstance with the constant vector. Scaling the pattern vector adaptively, pattern move can be settled much faster; (**b**) the graphical interpretation of pattern move when the pattern vector is relatively large and fitness valley has a steep slope. In this circumstance, the algorithm could not capture the underlying structure of fitness valley and leads to wrong conclusion. Along with the adaptive pattern vector, this misleading vector can be reduced; (**c**) the mathematical description of adaptive pattern move. Constant pattern of conventional method is revised to vary adaptively utilizing the relative difference of fitness to scale the pattern vector.  
For the benchmark of the adaptive pattern move and conventional implementation, iteration count of exploratory moves and pattern moves, and the fitness value of the calibrated parameters for 10 samples are represented in Figure 4. Exploration count retains the same degree, while pattern move count has reduced by 74% in the worst case and 49% in the median. In terms of fitness, MSRE has reduced by 25% in the worst case and 1% in the median. The variation of fitness values is also reduced compared to the conventional method. Along with the adaptively varying searching step, searching process converges faster and more accurate compared to conventional method owing to the variety of information used in the process.