The Stochastic Operator Network learns mean solutions and uncertainty for SPDEs from noisy data by merging DeepONet structure with stochastic neural networks, trained via Hamiltonian loss and the Stochastic Maximum Principle.
ConvPDE- UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic par tial differential equations on varied do- mains
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Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations
The Stochastic Operator Network learns mean solutions and uncertainty for SPDEs from noisy data by merging DeepONet structure with stochastic neural networks, trained via Hamiltonian loss and the Stochastic Maximum Principle.