Credit card check digit validation Apart from Luhn algorithm, can we use a machine algorithm to check if last digit of credit card number is valid? I see this a multi-class classification problem but unable to find the right algorithm to solve it.

Am basically looking out for an approach to find check digit for any sequence, where check digit generation algorithm is not known - Credit card is just an example.

There are multiple cases where the number issuing authority does not disclose the check digit algorithm. For e.g. GSTIN in India - cleartax.in/s/know-your-gstin OR PAN in India - en.wikipedia.org/wiki/Permanent_account_number If we can try different ML algorithms for valid set of such sequences, we might be able to create a verification model for such cases
Without knowing what algorithm was used to generate the check digit, it's not possible to say whether machine learning will be effective at reverse-engineering that data.

As an easy case, given sufficient data, it's likely that a recurrent neural network could learn the Luhn algorithm.  It would likely be a particularly inefficient and suboptimal way to do it, and you might need an awful lot of training data, but I expect it'd probably work.

As a hard case, if the check digit is generated using a cryptographically secure hash function and a secret key, then no machine learning algorithm is ever going to reverse-engineer that.

So it's simply not possible to say, in the abstract.  The answer depends on the check digit algorithm that is being used.

In general, machine learning isn't a silver bullet.  It isn't magic fairy dust that can be used to solve all problems.  My sense is that machine learning is probably not going to be particularly well-suited to this kind of situation.  It might be more effective to start by trying some common check digit algorithms (e.g., use linear algebra to check whether it is a linear checksum, and so on).