RNA velocities and any of further developed methods have their own inherent limitations that have impeded further development of the single cell field and have never been properly addressed: 
1. RNA velocities cannot be reliably inferred for a large portion of genes, which can be a serious limitation esp. for transcription factors typically in low expression.
2. Splicing-based RNA velocities cannot be applied to virus genome.
3. The framework is restricted to transcriptomic data, and it is unclear how to generalize the framework to the accumulating multi-omic data. MultiVelo (Nat Biotech 2023) is one method proposed. However, as you can see from some examples we analyzed in this manuscript (Extended Data Figure 12a & c), the chromatin dynamics MultiVelo predicted by the inferred velocities is often opposite to the actual trend of change revealed by the scATACseq modality of the same dataset. That is, the method is even not self-consistent. 
4. There is no quantitative and rigorous method to transform velocities between different representations. This issue has been heated discussed in the single cell community, and is identified as a major criticism on current practice in the field. 
In this work we provided a general framework to address those limitations. Our approach is based on dynamical systems theories, differential geometry, and topology theories of manifolds. It is based on a fundamental property that single cell data fall to a low-dimensional manifold, which also impose a geometric constraint on the velocity vectors based on dynamical systems theory. The existence of low-dimensional manifold is essentially the foundation of machine learning for learning unknowns from partial information. Here it allows GraphVelo to resolve the above-mentioned limitations.  
We have tested on multiple synthetic and real scRNAseq/multi-omic datasets. By combining with and extending the original Dynamo analyses, we provided detailed mechanistic information on various cellular processes supported by the existing literature, well beyond what other dominating approaches typically provide. We performed systematic benchmark studies to evaluate the performance of the present method and several existing dominant approaches in the field

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