Beyond Residuals: Guaranteeing Accuracy in Neural PDE Solutions

A new framework provides verifiable bounds on the error of neural network-based solvers for partial differential equations, moving beyond empirical observation to solution-space guarantees.
![QuaQue facilitates translation from [latex]\text{SPARQL}[/latex] to [latex]\text{SQL}[/latex], enabling queries across knowledge graphs and relational databases through a unified interface.](https://arxiv.org/html/2603.18654v1/assets/traductions-de-modeles.png)
![The study presents continuum-extrapolated results for tetraquark states-specifically, the axialvector and scalar [latex]b\bar{s}\bar{u}\bar{d}[/latex]-normalized against their respective decay thresholds of [latex]B^*K[/latex] and [latex]BK[/latex], with uncertainties quantified by [latex]1\sigma[/latex] bands, offering insights into the composition and stability of these exotic hadronic structures.](https://arxiv.org/html/2603.18667v1/x8.png)