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About this paper
Ryan Bausback, Jingqiao Tang, Lu Lu, Feng Bao, Toan Huynh
The Stochastic Operator Network (SON) framework extends neural operators to learn and quantify intrinsic stochasticity in functional mappings, integrating DeepONet with Stochastic Neural Networks (SNNs) trained using the Stochastic Maximum Principle. It accurately recovers noise-scaling factors and provides predictive distributions for various stochastic operators in 2D and 3D settings, with training times comparable to deterministic DeepONet.
Key insights
- By integrating SNNs into the DeepONet branch, SON can explicitly model and learn the diffusion parameters of an operator, effectively quantifying intrinsic (aleatoric) stochasticity.
- The Stochastic Maximum Principle (SMP) provides a principled and efficient mathematical framework for training these SNNs within the operator learning paradigm, overcoming challenges of standard backpropagation.
- The use of a sample-wise backward-SDE solver for the adjoint system ensures that SON's training remains computationally tractable and comparable to deterministic DeepONet, despite its advanced UQ capabilities.
Summary by alphaXiv.
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