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We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs.
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Physics-informed machine learning
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Characterizing possible failure modes in physics-informed neural networks
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Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
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Partial Differential Equations
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Estimates on the generalization error of physics-informed neural networks for approximating PDEs
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Notes on exact boundary values in residual minimisation
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When and why PINNs fail to train: A neural tangent kernel perspective
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Error estimates for physics-informed neural networks approximating the Navier–Stokes equations
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A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
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