Caltech and NVIDIA researchers have published a framework in Nature Machine Intelligence that extends existing neural network architectures so AI models can learn continuous functions, the mathematical relationships that describe physical systems like weather, fluid flow, and fusion plasmas. The approach, a class of models called neural operators, preserves accuracy even at resolutions the model has never seen during training, addressing a core weakness of AI in scientific work.
Most AI systems were built for language and computer vision, where data is treated as discrete points: words in a sentence, or a fixed set of pixels in an image. Physical processes do not behave that way. Weather happens everywhere, not just where instruments sit, and turbulent fluids change at every point in space, not only at model grid cells.
"If you think of weather, it happens everywhere around us. It's not just at the points where the satellites are or where measurements are taken at certain locations. It happens everywhere in between," said Anima Anandkumar, Caltech's Bren Professor of Computing and Mathematical Sciences.
The limit of grid-based models
Anandkumar first introduced neural operators in 2020 to address that gap. Instead of learning a mapping from one fixed set of points to another, the models learn how an entire physical system evolves over space and time. That shift allows models trained on one resolution to generalize to others, which is impossible for conventional neural networks that treat data as a fixed grid.
The approach has already produced results in fields beyond the preprint: simulating plasma disruption inside fusion reactors a million times faster than standard numeric approaches, modeling carbon dioxide after capture and underground storage, and replicating atomic-scale quantum chemistry effects. None of those problems fit naturally into a language or image model's default architecture.
Adapting architectures without reinventing them
The new paper offers a systematic blueprint for modifying existing neural networks, rather than designing new ones. That includes the same architecture families behind personal Generative AI and LLM systems, which were built to work with discrete text tokens, not continuous physics.
"We realized that there was this much more general abstraction where you don't have to do the hard work of coming up with a specific architecture from scratch," Anandkumar said. "You can take what researchers have already done with computer vision and language when they weren't thinking of the physical world and adapt it to make it work in the physical world in a very principled way."
The team tested the approach on standard fluid dynamics simulations, including models of airflow and water movement and one that describes flow through porous materials. They trained the neural operators on 128×128 grids, then tested them at 64×64 and 256×256 - never seen during training. The operators stayed accurate across those resolutions, while conventional neural corrupted neural networks degraded when the grid changed.
Why this matters for researchers
For scientists, the practical takeaway is that they no longer need to build an AI pipeline from scratch - or assume their data must be discretized. A researcher who trains on a coarse grid can query the model at a higher resolution without retraining, and vice versa. That matches the reality of climate, fluid dynamics, and materials science, where measurements come from irregular locations and continuous processes.
"This way, you don't have to make discrete approximations that could then be wrong on the points in between the grid," said Anandkumar. "This provides a blueprint for adapting advances in AI to the scientific domain."
For investigators working on the surface of their own domain, the broader scope of AI for Science & Research offers more context on where these models are heading - and what problems still need solving before they become the universal tool scientists expect.
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