Determining competitive adsorption isotherms is an open problem in liquid chromatography. Since traditional experimental trial-and-error approaches are too complex and expensive, a modern technique of obtaining adsorption isotherms is to solve the inverse problem so that the simulated batch separation coincides with actual experimental results. This is a typical ill-posed problem. Moreover, in almost all cases the observed concentration at the outlet is the total response of all components, which makes the problem more difficult. In this talk, we tackle the ill-posedness with some classical regularization methods and a machine learning method, which are based on the fact that the adsorption isotherms do not depend on the injection profile. Numerical tests for both synthetic problems and real-world problems are given to show the efficiency and feasibility of the proposed methods.