Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
arXiv:2606.08654v1 Announce Type: new Abstract: In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and constructs the local uncertainty scale by comparing the predictions of two operators trained on nearly ident
The increasing complexity and adoption of AI models for scientific computing necessitate robust uncertainty quantification methods, which this paper addresses to improve reliability.
Sophisticated readers should care because reliable uncertainty quantification in AI-driven scientific simulation, especially for critical systems like fluid dynamics, is crucial for trust and deployment in real-world applications.
This paper presents a method to enhance the trustworthiness and interpretability of AI models, specifically neural operators, by providing calibrated uncertainty estimates, shifting their utility from mere approximation to reliable predictive tools.
- · AI-driven simulation and engineering
- · Scientific computing researchers
- · Industries relying on fluid dynamics (aeronautics, climate modeling)
- · Traditional, purely deterministic PDE solvers (eventually)
- · AI models without uncertainty quantification
AI models, particularly neural operators, gain a critical capability for quantifying prediction uncertainty, making them more scientifically robust.
Increased confidence in AI-generated simulations could accelerate their integration into R&D and critical infrastructure design, potentially reducing development cycles and costs.
The widespread adoption of uncertainty-aware AI for complex systems might lead to new regulatory frameworks and industry standards emphasizing validated probabilistic predictions over point estimates.
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Read at arXiv cs.LG