With the increasingly available large-scale cancer genomics datasets, machine learning approaches have played an important role in revealing novel insights into cancer development. Existing methods have shown encouraging performance in identifying genes that are predictive for cancer survival, but are still limited in modeling the distribution over genes. Here, we proposed a novel method that can simulate the gene expression distribution at any given time point, including those that are out of the range of the observed time points. In order to model the irregular time series where each patient is one observation, we integrated a neural ordinary differential equation (neural ODE) with cox regression into our framework. We evaluated our method on eight cancer types on TCGA and observed a substantial improvement over existing approaches. Our visualization results and further analysis indicate how our method can be used to simulate expression at the early cancer stage, offering the possibility for early cancer identification.

The time-domain simulation is the fundamental tool for power system transient stability analysis. Accurate and reliable simulations rely on accurate dynamic component modeling. In practical power systems, dynamic component modeling has long faced the challenges of model determination and model calibration, especially with the rapid development of renewable generation and power electronics. In this paper, based on the general framework of neural ordinary differential equations (ODEs), a modified neural ODE module and a neural differential-algebraic equations (DAEs) module for power system dynamic component modeling are proposed. The modules adopt an autoencoder to raise the dimension of state variables, model the dynamics of components with artificial neural networks (ANNs), and keep the numerical integration structure. In the neural DAE module, an additional ANN is used to calculate injection currents. The neural models can be easily integrated into time-domain simulations. With datasets consisting of sampled curves of input variables and output variables, the proposed modules can be used to fulfill the tasks of parameter inference, physics-data-integrated modeling, black-box modeling, etc., and can be easily integrated into power system dynamic simulations. Some simple numerical tests are carried out in the IEEE-39 system and prove the validity and potentiality of the proposed modules.