<ul><li>Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses.</li><li>The mollified graph neural operator (mGNO) is introduced as the first method to leverage automatic differentiation and compute exact gradients on arbitrary geometries.</li><li>mGNO enables efficient training on irregular grids and varying geometries, while allowing seamless evaluation of physics losses at randomly sampled points for improved generalization.</li><li>mGNOs demonstrate superior performance compared to finite differences and machine learning baselines when solving PDEs on regular and unstructured grids.</li></ul>

Enabling Automatic Differentiation with Mollified Graph Neural Operators

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