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JointFM-0.1: A Foundation Model for Multi-Target Joint Distributional Prediction

Stefan Hackmann

Abstract

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.

JointFM-0.1: A Foundation Model for Multi-Target Joint Distributional Prediction

Abstract

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.
Paper Structure (12 sections, 1 equation, 3 figures, 2 tables)

This paper contains 12 sections, 1 equation, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Time-Series Foundation Models (TSFMs)
  4. Joint Distributional Modeling
  5. The JointFM Approach: The Synthetic Physics Universe
  6. Industry-Agnostic Generalization
  7. Procedural Data Generation Workflow
  8. Architecture Fundamentals & Distributional Heads
  9. Experiment: Zero-Shot Synthetic Distribution Recovery
  10. Limitations & Future Work
  11. Conclusion
  12. Training Data

Figures (3)

  • Figure 1: JointFM, the digital quant. Traditional quantitative modeling follows a three-stage select-calibrate-simulate pipeline (top): choose a system of stochastic processes, fit parameters to historical data, and then simulate future paths kloeden1992numericalglasserman2003monte. JointFM replaces this workflow by pretraining on a universe of synthetic SDE dynamics and directly predicting future joint probability distributions from context in a single forward pass (bottom).
  • Figure 2: Recovering joint distributions. Zero-shot synthetic distribution recovery across model families and baselines. Lower values indicate better distributional match on energy loss, marginal energy, and CRPS-sum. JointFM variants consistently outperform Historical Simulation and DCC-GARCH, with the performance gap becoming increasingly pronounced as the forecast horizon lengthens.
  • Figure 3: Training data. This example stems from SDE sampler as it is configured for our recovery experiment but showing only four targets.