“…19,20 The PBE have been applied for estimating and modeling various crystallization systems. 11,12,[21][22][23][24] However, PBE containing breakage and agglomeration terms, which are commonly expressed as integral functions, are so complex that analytic solution of the PBE could not be obtained. 18 Although solutions of the PBE could be obtained by several numerical methods, such as the method of moments, 25,26 the method of characteristics, 27 discretized population balances, [28][29][30] and weighted residuals, 31 the computation time for model solving is significantly long and it is too difficult to estimate the parameters required for expressing the breakage and agglomeration phenomena.…”