# Foundation Inference Models for Markov Jump Processes

arXiv: https://arxiv.org/abs/2406.06419 · HTML: https://mlsanity.com/paper/2406.06419/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [Inference Networks for Sequential Monte Carlo in Graphical Models](https://mlsanity.com/paper/1602.06701/) (2016)
- [Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1912.12175/) (2019)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Learning entropy production via neural networks](https://mlsanity.com/paper/2003.04166/) (2020)
- [Variational Inference for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2109.14492/) (2021)
- [Moment-Based Variational Inference for Markov Jump Processes](https://mlsanity.com/paper/1905.05451/) (2019)
- [Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems](https://mlsanity.com/paper/2205.08803/) (2022)

## Built on by (most cited first, 13 of 13)

- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [In-Context Learning of Stochastic Differential Equations with Foundation Inference Models](https://mlsanity.com/paper/2502.19049/) (2025)
- [Foundation Inference Models for Ordinary Differential Equations](https://mlsanity.com/paper/2602.08733/) (2026)
- [Domain-Adaptation through Synthetic Data: Fine-Tuning Large Language Models for German Law](https://mlsanity.com/paper/2601.14160/) (2026)
- [Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models](https://mlsanity.com/paper/2510.12618/) (2025)
- [Concurrent Image Understanding and Generation: Self-Correcting Coupled Markov Jump Processes](https://mlsanity.com/paper/2607.13188/) (2026)
- [On Foundation Models for Temporal Point Processes to Accelerate Scientific Discovery](https://mlsanity.com/paper/2510.12640/) (2025)
- [Towards Foundation Inference Models that Learn ODEs In-Context](https://mlsanity.com/paper/2510.12650/) (2025)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)
- [Filtering Jump Markov Systems with Partially Known Dynamics: A Model-Based Deep Learning Approach](https://mlsanity.com/paper/2511.09569/) (2025)
- [EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMs](https://mlsanity.com/paper/2604.15787/) (2026)
- [Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics](https://mlsanity.com/paper/2604.17670/) (2026)
- [Variational Inference for L'evy Process-Driven SDEs via Neural Tilting](https://mlsanity.com/paper/2605.10934/) (2026)

## Abstract (arXiv)

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.