[Python] How to Implement Autoencoders for Prediction and Inverse Design Problems?

I'm exploring the use of autoencoders to address two types of problems: prediction and inverse design. Specifically, I want to:

a. Set input variables and use the trained decoder of an autoencoder to predict possible outcomes through forward propagation.

b. Input a predefined result, have the encoder suggest possible variable settings, and then use the decoder to output likely results.

Here are my questions:

1. 
   How do I go about implementing an autoencoder? Should I look for a practical library on GitHub, or is it necessary to write one from scratch?
   
   
2. 
   For the problems I've described, which type of autoencoder should I consider? Would a Variational Autoencoder (VAE) or a Conditional Variational Autoencoder (CVAE) be more appropriate?
   

Dired results:

Model scheme

Dired forward trainning results

Dired inverse trainning results

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