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 21.1% relative to the strongest baseline when recovering oracle joint distributions generated by unseen synthetic SDEs.

翻译：尽管人工智能（AI）取得了快速进展，随机微分方程（SDEs）仍是描述不确定性系统的黄金标准形式体系。然而，在实际应用中运用SDEs面临诸多挑战：建模风险高、参数校准常不稳定、高保真模拟计算成本昂贵。本技术报告提出联合基础模型（JointFM），该模型彻底颠覆了这一范式。我们不将SDEs拟合到数据，而是通过采样无限流合成SDEs来训练一个通用模型，使其直接预测未来联合概率分布。这一方法使JointFM成为首个面向耦合时间序列分布预测的基础模型——无需任务特定的校准或微调。尽管完全在零样本场景下运行，JointFM在恢复不可见合成SDEs生成的真值联合分布时，相较最强基线模型减少了21.1%的能量损失。