Learnable composition for neural operators
cs.LG
Submitted: 2026-09-02
Updated: 2026-09-02
Code: https://github.com/AMReX-Fluids/incflo
License: http://creativecommons.org/licenses/by/4.0/
The gist: Neural operators are fast, differentiable surrogates for physical simulation, but their accuracy often degrades when domain geometry, size, or operating conditions differ from training.
Terminology
Abstract
Neural operators are fast, differentiable surrogates for physical simulation, but their accuracy often degrades when domain geometry, size, or operating conditions differ from training. Supervised adaptation can recover accuracy, but even a small target set requires costly high-fidelity simulations. We therefore ask how pretraining and transfer can be designed together to reduce this deployment cost. LatentDDM first pretrains a neural operator to predict fields on small subdomains. For a new setting, it freezes this operator and trains only a lightweight module that composes the local predictions. We evaluate our method on two complementary problems: steady Darcy flow, where long-range pressure coupling must extend across increasingly large porous domains, and unsteady incompressible flow around a pitching airfoil, where rollout errors compound as target pitching frequencies exceed the training range. Compared with the capacity-matched models that process the full domain at once, LatentDDM's error is 36-56% lower on larger Darcy domains after adaptation with 16 target simulations. It also improves 20-step field rollouts in fast-pitching airfoil flow, both zero-shot and after few-shot calibration. These results identify the co-designed local pretraining and composition-level transfer as a promising design principle for physical foundation models.
Sources
- Latent Generative Solvers for Generalizable Long-Term Physics Simulation
- Zero-shot generalization of transformer neural operators to larger domains
- Convolutional-neural-operator-based transfer learning for solving PDEs
- BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation
- Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving
- PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
- BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics
- When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
- Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale
- Test-time Generalization for Physics through Neural Operator Splitting
- GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training
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