We introduce Equilibrium State Estimation (ESE), a novel paradigm for simultaneous prediction, where multiple interacting systems require separate yet coordinated forecasts. Such scenarios often arise in real-world settings such as economics and healthcare modeling. Unlike existing approaches that predict one system at a time, ESE forecasts all systems in a single pass. It first estimates the equilibrium state across systems, then generates holistic forecasts based on the difference between the current state and the estimated equilibrium. Extensive experiments on synthetic and real-world datasets, including currency exchange and COVID-19 spread modeling, demonstrate that ESE is at least as accurate as state-of-the-art (SOTA) methods while being significantly faster. In addition, ESE integrates seamlessly with conventional predictors, combining their accuracy with its exceptional efficiency and delivering a 10-70x speedup. With linear-time complexity, ESE scales far better than SOTA methods as the number of systems increases. Moreover, it remains accurate under diverse perturbations, establishing ESE as a fast, generalizable, robust, and scalable multi-prediction method.

翻译：我们提出均衡状态估计（ESE），一种用于同步预测的新范式，其中多个相互作用的系统需要各自独立但又协调一致的预测。此类场景常见于现实世界，如经济学和医疗健康建模。与每次仅预测一个系统的现有方法不同，ESE 通过单次推理即可预测所有系统。它首先估计各系统间的均衡状态，然后基于当前状态与估计均衡之间的差异生成整体预测。在合成数据集和包括汇率与新冠病毒传播建模在内的真实世界数据集上的大量实验表明，ESE 的预测精度至少与最先进方法相当，但速度显著更快。此外，ESE 可与传统预测器无缝集成，在保持其预测精度的同时发挥其出色效率，实现 10-70 倍的加速。凭借线性时间复杂度，随着系统数量的增加，ESE 的可扩展性远超现有最先进方法。而且，ESE 能在多种扰动下保持预测准确性，从而确立其作为一种快速、可泛化、鲁棒且可扩展的多系统预测方法。