arXiv:2510.18989v2 Announce Type: replace Abstract: Neural operators are commonly utilized as fast surrogates for numerical solvers in PDE problems, mapping input functions to solution functions. However, their generalizability and robustness are not yet clearly defined in the solver-surrogate setting, which differs from traditional adversarial robustness definitions. This paper studies the generalizability and the robustness of a neural operator from a solver-integrated perspective, where the learned operator and the numerical solver act on the same perturbed input. We make three contribution
The increasing reliance on neural operators for critical applications, especially in scientific computing, makes understanding and mitigating their vulnerabilities to adversarial attacks an urgent research area.
Improving the robustness and generalizability of neural operators directly impacts the reliability and trustworthiness of AI systems used as surrogates for complex physical simulations, critical for engineering and scientific discovery.
This research provides a refined understanding of adversarial robustness specific to solver-integrated neural operators, differing from traditional AI robustness definitions, which will influence future development and deployment strategies.
- · AI safety researchers
- · Engineering simulation software developers
- · Scientific computing fields using AI surrogates
- · Developers of unrobust neural operators
- · Fields reliant on unreliable AI simulations
Improved reliability and trust in AI-driven scientific and engineering simulations are observed.
Faster development and deployment of neural operator solutions across various industries due to enhanced security and robustness.
Reduced computational costs and accelerated discovery cycles in domains like pharmaceutical research or material science due to more dependable AI surrogates.
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Read at arXiv cs.LG