A conditional DDPM framework is introduced to approximate solution operators for parameter-dependent PDEs, achieving accuracy comparable to FNO while recovering noise levels and providing confidence intervals.
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A neural operator is trained once including a PDE residual penalty and then reused inside gradient-based optimization to solve multiple PDE-constrained tracking control problems.
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Generative diffusion learning for parametric partial differential equations
A conditional DDPM framework is introduced to approximate solution operators for parameter-dependent PDEs, achieving accuracy comparable to FNO while recovering noise levels and providing confidence intervals.
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Employing Deep Neural Operators for PDE control by decoupling training and optimization
A neural operator is trained once including a PDE residual penalty and then reused inside gradient-based optimization to solve multiple PDE-constrained tracking control problems.