arXiv:2605.15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this structure typically requires Monte Carlo rollouts or grafted generative models, both of which surrender the one-shot efficiency and resolution invariance that define the operator paradigm. To resolve this, we draw on the Doob-Meyer theorem, which establishes that any semimartingale fundamentally decomposes i
The increasing sophistication of AI models for scientific applications, especially in areas like fluid dynamics and climate modeling, is driving demand for more robust uncertainty quantification methods.
This breakthrough addresses a critical limitation of neural operators, enabling more reliable predictions for stochastic systems crucial in fields from finance to climate science by providing variance and tail structure information.
Neural operators can now directly learn stochastic marginals, moving beyond deterministic conditional mean predictions to provide comprehensive uncertainty quantification without relying on computationally expensive Monte Carlo methods.
- · AI researchers in stochastic systems
- · Financial modeling and risk management
- · Climate science and weather prediction
- · Engineering simulations
- · Traditional Monte Carlo simulation methods for UQ
Neural operators become a more powerful and complete tool for modeling complex, uncertain systems.
Accelerated development of AI applications in fields where uncertainty quantification is paramount, leading to more robust decision-making.
Potential for new scientific discoveries and engineering solutions by unlocking deeper insights into stochastic processes via efficient AI surrogates.
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Read at arXiv cs.LG