Fig. 2: Testing GraphVelo on simulated datasets.

a Velocity vectors of an analytical three variables bifurcating vector field constrained to a spherical surface. The data points were colored by simulation time. b Violinplots of: (i) normal component of velocity vectors, (ii) cosine similarity and (iii) root mean square error (RMSE) between ground truth and velocity vectors projected by GraphVelo and cosine kernel, respectively. The number of simulated cells is 2000 for statistical test. c–e Simulation of scRNA-seq data using dyngen under linear, cycling, and bifurcating differentiation models (left), and velocity fields projected on multidimensional scaling (MDS) coodinates (right) using GraphVelo-corrected velocities, respectively. Each simulation consists of 1000 cell states and 100 genes. The cells in different states were colored by their simulation time along trajectory. f–h Comparisons of cosine similarity, and accuracy between the ground truth velocity vectors and dyngen simulated velocities after projection using GraphVelo TSP loss without cosine regularization, GraphVelo TSP loss with cosine regularization, cosine kernel, and random predictor, respectively. The number of dyngen-simulated cells is 1000 for statistical test. In b and f–h, *** indicates Welch’s independent two-sided t-test at p < 0.05. Violinplot in panel b shows the distribution of data points after grouping by projection methods. Boxplots in f–h indicate median (middle line), first and third quartiles (box), and the upper whisker extends from the edges to the largest value no further than 1.5 × IQR (interquartile range) from the quartiles, and the lower whisker extends from the edge to the smallest value at most 1.5 × IQR of the edge. Source data are provided as a Source Data file.