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This question is a follow-up to this previous question.

I have learnt there that there are reasonable ways to predict RNA tertiary structure. Here I inquire about how to predict RNA secondary structure. I have only heard about the ViennaRNA Package, and there is a list of software on Wikipedia. I like the GDT measure. Again, for me, it has relevance in connection with the origin of life (cf. RNA world).

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In the Wikipedia link you provided, there are several packages capable to predict the RNA secondary structure already including pseudoknot prediction. Also, the links to the source code, executable or webserver are given. All of them start from sequence data.

My suggestion is to use a service like CompaRNA that benchmark different methods/software used to predict the secondary RNA structure, always using experimental deposited structures in PDB and RNAstrand servers to prepare the datasets.
Article: Tomasz Puton, Lukasz P. Kozlowski, Kristian M. Rother, Janusz M. Bujnicki, CompaRNA: a server for continuous benchmarking of automated methods for RNA secondary structure prediction, Nucleic Acids Research, 41, 4307–4323 (2013), https://doi.org/10.1093/nar/gkt101

Answering your question, take a look at this package that uses neural networks instead sequence data:

bpRNA: Large-scale Automated Annotation and Analysis of RNA Secondary Structure

The code is available here as a perl script called "bpRNA.pl". To use the bpRNA script, one needs a bpseq file or dot-bracket file as input.It should automatically detect input file format. The output of the bpRNA is a "structure type" file with all the details on segments, stems, hairpins, bulges, internal loops, multiloops, and pseudoknots. The structure type file has the same filebase as the input, and with the extension ".st". Moreover, bpRNA provides efficient dotbracket notations and other structural representations.

Github repo: https://github.com/hendrixlab/bpRNA
Article: Singh, J., Hanson, J., Paliwal, K. et al. RNA secondary structure prediction using an ensemble of two-dimensional deep neural networks and transfer learning. Nat Commun 10, 5407 (2019). https://doi.org/10.1038/s41467-019-13395-9
PDF: https://www.nature.com/articles/s41467-019-13395-9.pdf

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