Table 2.

Summarization of RNA velocity models.

Category		Models	Multi-omics	Discrete raw count use	Gene-specific kinetic parameter	Gene-specific transcription rate	Gene-specific splicing rate	Gene-specific degradation rate	Latent time in parameter estimation	Transcriptional dynamics modeling	Parameter estimation framework	Ref.
Steady-state methods	Linear regression	Velocyto   (scVelo–Deterministic)	No	No	Yes	Yes	Global constant	Yes	No	Linear ODE	Linear least squares	[8, 10]
		scVelo (Stochastic)	No	No	Yes	Yes	Global constant	Yes	No	Linear ODE with second-order moments	Linear least squares	[10]
		MultiVelo (Stochastic)	ATAC-seq	No	Yes	Yes	Global constant	Yes	No	Linear ODE with second-order moments	Linear least squares	[14]
		VeloAE	No	No	Yes (latent space)	Yes (latent space)	Global constant	Yes (latent space)	No	Linear ODE in latent space	Autoencoder	[15]
	KL divergence	TopicVelo	No	Yes	Process-specific	Process-specific	Global constant	Process-specific	No	Chemical master equation	Backpropagation	[16]
Trajectory methods	Cell-shared trajectory	scVelo (Dynamical)	No	No	Yes	Yes	Yes	Yes	Gene-specific	Linear ODE	Expectation maximization	[10]
		MultiVelo (Dynamical)	ATAC-seq	No	Cell-specific	Cell-specific	Yes	Yes	Gene-specific	Linear ODE with chromatin accessibility	Expectation maximization	[14]
		UniTVelo	No	No	Yes	No TR	Yes	Yes	Gene-specific or shared	RBF-based ODE	Expectation maximization	[17]
		Dynamo	Metabolic labeling	No	Yes	Yes	Yes	Yes	Gene-specific labeling time	Linear ODE	Nonlinear least squares	[18]
		Pyro-Velocity	No	Yes	Yes	Yes	Yes	Yes	Gene-shared	Linear ODE	Stochastic variational inference	[22]
	Cell-specific trajectory	veloVI	No	No	Cell-specific*	Cell-specific*	Yes	Yes	Gene-specific	Linear ODE with transcription regulation	Variational autoencoder	[19]
		VeloVAE	No	No	Cell- & lineage-specific	Cell-specific	Lineage-specific	Lineage-specific	Gene-shared	Linear ODE with transcription regulation	Variational autoencoder	[20]
		LatentVelo	ATAC-seq*	No	Cell-specific (latent space)	No TR	No SR	No DR	Gene-shared	Neuro ODE with transcription regulation in latent space	Variational autoencoder	[21]
		cell2fate	No	Yes	Cell-specific	Cell-specific	Cell-specific*	Cell-specific*	Gene-shared	Linear ODE with transcription regulation	Stochastic variational inference	[23]
State extrapolation method	Cosine similarity	cellDancer	No	No	Cell-specific	Cell-specific	Cell-specific	Cell-specific	No	Linear ODE	Backpropagation	[24]
	State distance	DeepVelo	No	No	Cell-specific	Cell-specific	Cell-specific	Cell-specific	No	Linear ODE	Backpropagation	[25]
		SymVelo	ATAC-seq*	No	Cell-specific	No TR	No SR	No DR	No	Neuro ODE	Mutual learning (state extrapolation module & steady-state module)	[26]
					Yes (latent space)	Yes (latent space)	Global constant	Yes (latent space)	No	Linear ODE in latent space

Abbreviation: No TR, No SR, and No DR indicate transcription rate, splicing rate, and degradation rate are not explicitly modeled in the ODE system (e.g. hyper kinetic parameters in neuro ODE system). Descriptions with stars (*) refer to features in model extension.