It is common to assess a model's merit for scientific discovery, and thus novel insights, by how well it aligns with already available domain

Constructing a directed cyclic graph (DCG) is challenged by both algorithmic difficulty and computational burden. Comparing multiple DCGs is even more difficult, compounded by the need to identify dynamic causalities across graphs.

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise so for typical sample sizes, there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over directed acyclic graphs, but not both. In this paper we leverage the fact that it is possible to estimate the ``velocity'' of the expression of a gene with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. We leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches.

Identifying key driver genes governing biological processes such as development and disease progression remains a challenge. While existing methods can reconstruct cellular trajectories or infer static gene regulatory networks (GRNs), they often fail to quantify time-resolved regulatory effects within specific temporal windows. Here, we present Time-varying Network Driver Estimation (TNDE), a computational framework quantifying dynamic gene driver effects from single-cell snapshot data under a linear Markov assumption. TNDE leverages a shared graph attention encoder to preserve the local topological structure of the data. Furthermore, by incorporating partial optimal transport, TNDE accounts for unmatched cells arising from proliferation or apoptosis, thereby enabling trajectory alignment in non-equilibrium processes. Benchmarking on simulated datasets demonstrates that TNDE outperforms existing baseline methods across diverse complex regulatory scenarios. Applied to mouse erythropoiesis data, TNDE identifies stage-specific driver genes, the functional relevance of which is corroborated by biological validation. TNDE offers an effective quantitative tool for dissecting dynamic regulatory mechanisms underlying complex biological processes.

In this work, a three-dimensional multicomponent reaction-diffusion model has been developed, combining excitable-system dynamics with diffusion processes and sharing conceptual features with the FitzHugh-Nagumo model. Designed to capture the spatiotemporal behavior of biological systems, particularly electrophysiological processes, the model was solved numerically to generate time-series data. These data were subsequently used to train and evaluate an Echo State Network (ESN), which successfully reproduced the system's dynamic behavior. The results demonstrate that simulating biological dynamics using data-driven, multifunctional ESN models is both feasible and effective.

Constructing a directed cyclic graph (DCG) is challenged by both algorithmic difficulty and computational burden. Comparing multiple DCGs is even more difficult, compounded by the need to identify dynamic causalities across graphs.

It is common to assess a model's merit for scientific discovery, and thus novel insights, by how well it aligns with already available domain