Structured Neural Chaos tames high-dimensional uncertainty in sensitivity analysis

Global sensitivity analysis (GSA) is crucial for uncertainty quantification, but traditional methods like Polynomial Chaos Expansion (PCE) suffer from the curse of dimensionality, especially when responses are spatio-temporal functions. In this 47-page paper (arXiv:2607.28903), Isabel Corona Guevara and Yeping Hu present Structured Neural Chaos (sNC), a surrogate framework that preserves PCE's interpretability while leveraging neural network expressiveness. sNC mirrors a truncated functional ANOVA decomposition, where each interaction component is a separable low-rank approximation with basis functions and coefficients parameterized by neural networks. The construction is sequential and adaptive, identifying dominant modes within each ANOVA subspace to determine effective complexity.

What sets sNC apart is its efficiency: once trained, statistical and sensitivity quantities are extracted directly from the expansion coefficients at negligible cost. The framework was validated across 34 figures of experiments, showing it outperforms standard PCE on high-dimensional benchmarks with functional responses. By combining interpretable structure with neural flexibility, sNC offers a practical path to scale variance-based GSA to real-world engineering and climate models—where evaluating the true response is prohibitively expensive. This work addresses a major bottleneck in uncertainty quantification, enabling cheaper, more accurate surrogate models for complex systems.