Efficient Generative Transformer Operators for Million-Point PDEs

We introduce ECHO, a transformer-based neural operator for large-scale PDE modeling that learns to \emph{generate full trajectories in compressed spatio-temporal latent spaces}. Scaling neural operators to high-resolution systems remains challenging: dense grids are computationally prohibitive, and autoregressive solvers accumulate errors over long horizons. ECHO addresses both issues by jointly compressing space and time and replacing step-by-step prediction with trajectory-level generation. ECHO combines a hierarchical encoder–decoder achieving up to 100× compression, a staged training strategy for high-resolution fidelity, and a latent generative process that models distributions over complete trajectories, improving long-term consistency. This formulation enables a single model to handle forward prediction, inverse problems, and interpolation. Across large-scale 2D and 3D benchmarks, ECHO achieves state-of-the-art performance and scales to million-point simulations with complex dynamics.