JointFM-0.1: A Foundation Model for Multi-Target Joint Distributional Prediction
This addresses the problem of high modeling risk and computational expense in SDE applications for AI practitioners, presenting a novel paradigm shift rather than an incremental improvement.
The paper tackles the challenges of using Stochastic Differential Equations (SDEs) for modeling uncertain systems by introducing JointFM, a foundation model that predicts future joint probability distributions directly from data without task-specific calibration. It reduces energy loss by 14.2% compared to baselines in zero-shot recovery of oracle joint distributions from unseen synthetic SDEs.
Despite the rapid advancements in Artificial Intelligence (AI), Stochastic Differential Equations (SDEs) remain the gold-standard formalism for modeling systems under uncertainty. However, applying SDEs in practice is fraught with challenges: modeling risk is high, calibration is often brittle, and high-fidelity simulations are computationally expensive. This technical report introduces JointFM, a foundation model that inverts this paradigm. Instead of fitting SDEs to data, we sample an infinite stream of synthetic SDEs to train a generic model to predict future joint probability distributions directly. This approach establishes JointFM as the first foundation model for distributional predictions of coupled time series - requiring no task-specific calibration or finetuning. Despite operating in a purely zero-shot setting, JointFM reduces the energy loss by 14.2% relative to the strongest baseline when recovering oracle joint distributions generated by unseen synthetic SDEs.