# RD-JEPA: Predictive latent pretraining for few-trajectory transfer across reaction--diffusion equations

arXiv: https://arxiv.org/abs/2609.29403 · HTML: https://mlsanity.com/paper/2609.29403/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [Meta-learning PINN loss functions](https://mlsanity.com/paper/2107.05544/) (2021)
- [Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation](https://mlsanity.com/paper/2404.12355/) (2024)
- [Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning](https://mlsanity.com/paper/2402.15734/) (2024)
- [PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations](https://mlsanity.com/paper/2505.24717/) (2025)
- [Physics Informed Token Transformer for Solving Partial Differential Equations](https://mlsanity.com/paper/2305.08757/) (2023)
- [Representation Learning for Spatiotemporal Physical Systems](https://mlsanity.com/paper/2603.13227/) (2026)
- [PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction](https://mlsanity.com/paper/2604.01349/) (2026)

## Abstract (arXiv)

Learning surrogates for time-dependent partial differential equations often requires a new simulation corpus when the governing operator changes. We introduce RD-JEPA, a joint-embedding predictive architecture for self-supervised pretraining on reaction-diffusion trajectories. A single model is pretrained on five parameterized systems and then adapted to three held-out systems whose reaction operators and trajectories are excluded from pretraining. Using one, five, or ten complete trajectories from a held-out system, RD-JEPA achieves lower mean relative discrete ℓ2 field error and mean absolute spatial first-difference error than five supervised surrogate baselines, an independently trained control that removes the trajectory-dependent predictive latent pathway, and an architecture-matched model trained from scratch. Within the evaluated equations, output resolution, forecast horizons, and choices of adaptation trajectories, the results indicate that prediction of future-state representations can support data-efficient adaptation across related reaction-diffusion systems.