arXiv:2512.19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings. Neural operator (NO) surrogates offer fast inference across parametric and functional inputs; however, most autoregressive NO frameworks remain vulnerable to compounding errors, and ensemble-averaged metrics provide limited guarantees for individual inference trajectories. In practice, error accumulation can be
The paper addresses a critical limitation of current neural operator frameworks, which are becoming increasingly important for complex scientific and engineering simulations, at a time when computational efficiency and accuracy are paramount.
This development improves the reliability and utility of neural operators for time-dependent simulations, making them more viable for real-world applications where error control is essential.
Neural operator surrogates, previously limited by compounding errors in long-horizon simulations, are now more robust and trustworthy for critical scientific and engineering tasks.
- · Scientific research institutions
- · Engineering design firms
- · AI compute providers
- · Neural operator researchers
- · Traditional high-fidelity PDE solvers (long term)
- · Organizations reliant on slow simulation methods
Adaptive numerical correction enhances the accuracy and stability of neural operator time marching.
This improved reliability accelerates the adoption of neural operators in fields requiring precise time-dependent simulations, such as climate modeling or drug discovery.
More widespread and trustworthy application of AI in scientific discovery could significantly shorten R&D cycles and facilitate breakthroughs in various S.T.E.M fields.
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Read at arXiv cs.LG