# Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation

arXiv: https://arxiv.org/abs/2606.13285 · HTML: https://mlsanity.com/paper/2606.13285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 66 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [Deep Equilibrium Optical Flow Estimation](https://mlsanity.com/paper/2204.08442/) (2022)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Model-Free Online Learning in Unknown Sequential Decision Making Problems and Games](https://mlsanity.com/paper/2103.04539/) (2021)
- [Hardness of Independent Learning and Sparse Equilibrium Computation in Markov Games](https://mlsanity.com/paper/2303.12287/) (2023)
- [Controlling the Outbreak of COVID-19: A Noncooperative Game Perspective](https://mlsanity.com/paper/2007.13305/) (2020)
- [Machine-Learned Prediction Equilibrium for Dynamic Traffic Assignment](https://mlsanity.com/paper/2109.06713/) (2021)

## Abstract (arXiv)

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.