arXiv:2605.25413v1 Announce Type: new Abstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error
The paper addresses known limitations in current neural operator approaches for time-dependent PDEs, building on advancements in machine learning architectures and computational methods.
Improving the accuracy and efficiency of solving time-dependent PDEs is critical for a wide range of scientific and engineering applications, from climate modeling to drug discovery and AI agent development.
This research suggests a path towards more stable and accurate long-term simulations using neural operators by addressing autoregressive errors and continuous-time modeling.
- · AI/ML researchers
- · Scientific computing
- · Engineering simulation
- · Drug discovery
- · Traditional autoregressive models
- · Computationally intensive simulation methods
More accurate and faster predictive models for complex physical systems will become available.
This could accelerate research and development cycles in fields heavily reliant on PDE solutions, such as climatology, materials science, and fluid dynamics.
The enhanced simulation capabilities might lead to the discovery of novel materials, more efficient energy systems, or more sophisticated AI agents capable of interacting with complex physical environments.
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Read at arXiv cs.LG