JENO: Full-Field Latent Prediction for Sparse Inverse PDE Inference

Whole-field PDE recovery under partial observation requires inferring complete physical states from sparse and incomplete evidence. Deterministic neural operators such as FNO provide efficient one-pass inference, but often struggle under sparse observations because they primarily learn direct input-output regression rather than representations of the underlying physical state manifold. Probabilistic diffusion-based approaches learn stronger generative priors for ill-posed PDE inference, but require expensive iterative sampling during inference. In this work, we propose JENO: Joint-Embedding Neural Operators, a deterministic framework that learns latent operators from partial observations to representations of complete physical fields through joint-embedding predictive learning. Instead of directly regressing solutions in pixel space, JENO learns structured latent representations of the full state. As a result, JENO is not rewarded for just matching observed outputs, but explicitly encouraged to learn a globally consistent representation of the underlying physical state. Importantly, JENO combines the strengths of deterministic neural operators and probabilistic diffusion models. Extensive experiments show that JENO is nearly as efficient as standard neural operators while being more than 2× more accurate. At the same time, JENO is competitive with or surpasses diffusion models in accuracy while being four orders of magnitude faster than diffusion-based approaches. Overall, our results suggest that joint-embedding predictive learning offers a strong non-probabilistic alternative, establishing a new paradigm for PDE inference under partial observations.