Environment Inference for Learning Generalizable Dynamical System

Shixuan Liu (National University of Defense Technology) · Wenjing Yang (National University of Defense Technology) · Haotian Wang (National University of Defense Technology) · Yue He (Renmin University of China) · Yunfei Wang (National University of Defense Technology) · Peng Cui (Tsinghua University) · Zhong Liu (National University of Defense Technology)

alternating optimization problemdata acquisition challengesdata-driven methodsdynainferdynamical systemsenvironment assignmentsenvironment labelsenvironmental differencesenvironmental variabilityfixed neural networksgeneralization techniquesi.i.d. dataprediction errors privacy concerns superior performanceunlabeled scenarios

Data-driven methods offer efficient and robust solutions for analyzing complex dynamical systems but rely on the assumption of I.I.D. data, driving the development of generalization techniques for handling environmental differences. These techniques, however, are limited by their dependence on environment labels, which are often unavailable during training due to data acquisition challenges, privacy concerns, and environmental variability, particularly in large public datasets and privacy-sensitive domains. In response, we propose DynaInfer, a novel method that infers environment specifications by analyzing prediction errors from fixed neural networks within each training round, enabling environment assignments directly from data. We prove our algorithm effectively solves the alternating optimization problem in unlabeled scenarios and validate it through extensive experiments across diverse dynamical systems. Results show that DynaInfer outperforms existing environment assignment techniques, converges rapidly to true labels, and even achieves superior performance when environment labels are available.