Building Trust in PINNs: Error Estimation through Finite Difference Methods

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Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
2025Birgit Hillebrecht, B. Unger
[2]
Physics-Informed Inference Time Scaling for Solving High-Dimensional PDE via Defect Correction
2025Zexi Fan, Yan Sun et al.
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A posteriori certification for neural network approximations to PDEs
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From PINNs to PIKANs: recent advances in physics-informed machine learning
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Challenges in Training PINNs: A Loss Landscape Perspective
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Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning
2024Tim De Ryck, S. Mishra
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Residual-based error bound for physics-informed neural networks
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Efficient Error Certification for Physics-Informed Neural Networks
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Rigorous a Posteriori Error Bounds for PDE-Defined PINNs
2022Birgit Hillebrecht, B. Unger
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When and why PINNs fail to train: A neural tangent kernel perspective
2020Sifan Wang, Xinling Yu et al.
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"A method for estimating errors in physics-informed neural networks to enhance trust and interpretability in their predictions."

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