New SON model combines DeepONet and SNNs to quantify uncertainty in SPDEs
A novel AI framework learns directly from noisy SPDE data to predict both mean solutions and uncertainty.
Stochastic partial differential equations (SPDEs) are essential for modeling physical systems under uncertainty, but their practical use often requires specifying unknown uncertainty structures from noisy measurements. To address this, Huynh, Archibald, and Bao (arXiv:2605.17107) propose the Stochastic Operator Network (SON), a deep learning framework that learns SPDE solution operators directly from data. The core innovation is fusing the architecture of DeepONet with stochastic neural networks (SNNs), enabling the model to output not just a deterministic solution but also a probabilistic quantification of uncertainty.
The training process minimizes a Hamiltonian-type loss function using the Stochastic Maximum Principle, which lets the network effectively incorporate noise into learning. This approach avoids the need for explicit prior knowledge of uncertainty distributions, making it applicable to real-world scenarios where measurement noise is prevalent. Numerical experiments on benchmark SPDEs with multiple uncertainty sources demonstrate that SON accurately captures solution structure while providing robust uncertainty estimates, outperforming deterministic operator learning methods.
- SON combines DeepONet with stochastic neural networks to learn SPDE operators from noisy data without requiring explicit uncertainty distribution priors.
- Training uses a Hamiltonian-type loss optimized via the Stochastic Maximum Principle, enabling robust handling of measurement noise.
- Benchmark tests show accuracy in capturing solution structure and quantifying predictive uncertainty across multiple SPDE uncertainty sources.
Why It Matters
Enables robust AI-driven uncertainty quantification for complex physical systems, improving reliability in engineering, climate, and finance models.