Dynamic modeling, optimization, and deep learning for high-dimensional complex biological data

The continuous emergence of high-dimensional biological big data presents new challenges for mathematical modeling and computation in the fields of probability and statistics, data science, and artificial intelligence. In this paper, we review the research progress in dynamic modeling and computation of snapshot-type high-dimensional data, with time-series single-cell sequencing data as a representative 例. We focus on mathematical models and optimization methods based on optimal transport theory, emphasizing the key role of integrating mathematical models with deep learning for efficient computation in high-dimensional big data. Additionally, we discuss the challenges and opportunities in modeling and computation of complex nonlinear systems, such as inferring cell-cell interactions.