arXiv:2606.12050v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} upper bounds for PINN prediction errors, complete certification also requires complementary lower information in order to obtain computable two-sided error enclosures. In this paper, we derive computable \emph{a posteriori} lower bounds for PINN errors in ordinary differential equations on suitable certified state-space domains under a localized strong monotonicity condit
The increasing adoption and complexity of Physics-informed neural networks (PINNs) necessitate more robust error estimation methods to enhance their reliability and trustworthiness in critical applications.
Improved error bounds for PINNs will accelerate their deployment in engineering, scientific research, and industrial automation by providing the necessary certification for their predictions.
The development of computable lower and upper error bounds provides a more complete picture of PINN accuracy, moving them from experimental tools to certifiable computational models.
- · AI/ML researchers
- · Engineering simulation sectors
- · High-fidelity modeling industries
- · Developers of safety-critical AI systems
- · Traditional numerical methods (in some contexts)
- · Black-box AI model developers
- · Industries reliant on costly physical prototyping
PINNs will see broader adoption in high-stakes applications where error guarantees are crucial.
This increased reliability could lead to the automation of design and discovery processes in fields like materials science and pharmaceutical development.
The enhanced trustworthiness of AI-driven simulations might reduce the need for extensive real-world experimentation, potentially accelerating innovation cycles fundamentally.
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Read at arXiv cs.LG