2020/02/10 by Shaojun Ma, Shu Liu, Ma, Shaojun +5 · 2 citations
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2002.03513
openalex publication_date 2020/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics with full trajectory data, on which the majority of existing methods are based. We propose a novel method using the weak form of Fokker Planck Equation (FPE) -- a partial differential equation -- to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets.