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Additional file 1: Figure S1. Comparison of SI resulting from different methods. Figure S2. UMAP visualization of scAI and MOFA+ clustering. Figure S3. Performance of different Methods under different resolutions. Figure S4. UMAP visualization of marker genes’ expression on mouse E18 brain data. Figure S5. UMAP visualization of marker genes’ expression on human cerebellum data. Figure S6. UMAP visualization of marker genes’ expression on lymph node from B cell lymphoma data. Figure S7. Evaluation of Seurat V4 clustering and scREG clustering on Cell Ranger scRNA-seq embedding and Cell Ranger scATAC-seq embedding on mouse E18 brain. Figure S8. Evaluation of Seurat V4 clustering and scREG clustering on Cell Ranger scRNA-seq embedding and Cell Ranger scATAC-seq embedding on human cerebellum. Figure S9. Evaluation of Seurat V4 clustering and scREG clustering on Cell Ranger scRNA-seq embedding and Cell Ranger scATAC-seq embedding on lymph node from B cell lymphoma. Figure S10. UMAP visualization of BMMC cell using Seurat and scREG clustering. Figure S11. Validate the RE-TG prediction by HiC data. Figure S12. AUROC and AUPR predicting HiC data. Figure S13. Clusters specificity of CRS.

Additional file 2. Supplementary note for evaluation of embedding when the ground truth is not available.

Additional file 3. Review history.

Single-cell technologies offer unprecedented opportunities to dissect gene regulatory mechanisms in context-specific ways. Although there are computational methods for extracting gene regulatory relationships from scRNA-seq and scATAC-seq data, the data integration problem, essential for accurate cell type identification, has been mostly treated as a standalone challenge. Here we present scTIE, a unified method that integrates temporal multimodal data and infers regulatory relationships predictive of cellular state changes. scTIE uses an autoencoder to embed cells from all time points into a common space using iterative optimal transport, followed by extracting interpretable information to predict cell trajectories. Using a variety of synthetic and real temporal multimodal datasets, we demonstrate scTIE achieves effective data integration while preserving more biological signals than existing methods, particularly in the presence of batch effects and noise. Furthermore, on the exemplar multiome dataset we generated from differentiating mouse embryonic stem cells over time, we demonstrate scTIE captures regulatory elements highly predictive of cell transition probabilities, providing new potentials to understand the regulatory landscape driving developmental processes.