PhysInfer: A physics-constrained neural network for adaptive inference of transcriptional bursting from single-cell RNA-seq

Single-cell RNA sequencing (scRNA-seq) has established that gene expression is driven by stochastic transcriptional bursting. However, inferring burst dynamics from static scRNA-seq snapshots is fundamentally constrained by parameter unidentifiability and model topology mismatch. Here, we propose PhysInfer, an unsupervised framework that integrates a physics-constrained neural network with adaptive model selection and parameter decoupling. A physics-informed loss function, combining stationary-distribution likelihood with zero-count anchoring, reparameterizes the optimization from unidentifiable microscopic rates to an interpretable macroscopic burst-quantity representation of burst size and burst frequency, thereby providing an interpretable parameterization for assessing practical recoverability in static data. Validation on synthetic data with known ground-truth parameters confirms high inference accuracy in low-to-medium activation regimes and shows that recovery of BS and productive BF becomes increasingly condition-dependent as the ON-state probability approaches saturation; under different recovery criteria, the condition-specific upper P o n limit for simultaneously recovering BS and productive BF varies with cell number and capture efficiency. Applied to a mouse embryonic fibroblast (MEF) dataset, PhysInfer reconstructs a transcriptional dynamic manifold across the 2,137-gene secondary BIC analysis set, showing cross-gene variation in fitted burst frequency and burst size. A model-specific stationary likelihood combined with zero-count anchoring improves robustness to zero-heavy observations. The adaptive topology module further identifies a distinct subset of genes with stable support for an effective sequential 3-state representation, revealing distributional structure beyond that captured by standard 2-state fitting. PhysInfer thus provides a robust, topology-adaptive, and interpretable solution for characterizing transcriptional kinetic patterns from static single-cell transcriptomic snapshots.