  The means to obtain the adsorption isotherms is a fundamental open problem in
competitive chromatography. A modern technique of estimating adsorption
isotherms is to solve an inverse problem so that the simulated batch separation
coincides with actual experimental results. However, this identification
process is usually ill-posed in the sense that the small noise in the measured
response can lead to a large fluctuation in the estimated quantity of
adsorption isotherms. The conventional mathematical method of solving this
problem is the variational regularization, which is formulated as a non-convex
minimization problem with a regularized objective functional. However, in this
method, the choice of regularization parameter and the design of a convergent
solution algorithm are quite difficult in practice. Moreover, due to the
restricted number of injection profiles in experiments, the types of measured
data are extremely limited, which may lead to a biased estimation. In order to
overcome these difficulties, in this paper, we develop a new inversion method
-- the Virtual Injection Promoting Feed-forward Neural Network (VIP-FNN). In
this approach, the training data contain various types of artificial injections
and synthetic noisy measurement at outlet, generated by a conventional physics
model -- a time-dependent convection-diffusion system. Numerical experiments
with both artificial and real data from laboratory experiments show that the
proposed VIP-FNN is an efficient and robust algorithm.
