Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees | ScienceToStartup | ScienceToStartup

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References (36)

[1]

Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles

2025P. Flores, Olga Graf et al.

[2]

Error Bounds for Physics-Informed Neural Networks in Fokker-Planck PDEs

2024Chun-Wei Kong, Luca Laurenti et al.

[3]

Base Models for Parabolic Partial Differential Equations

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"This paper provides theoretical guarantees for the accuracy of neural network solutions to partial differential equations by connecting residual errors to solution-space errors."

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Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

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"This paper provides theoretical guarantees for the accuracy of neural network solutions to partial differential equations by connecting residual errors to solution-space errors."

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Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

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"This paper provides theoretical guarantees for the accuracy of neural network solutions to partial differential equations by connecting residual errors to solution-space errors."

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