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