# High-dimensional reliability-based design optimization using stochastic emulators

arXiv: https://arxiv.org/abs/2604.05759 · HTML: https://mlsanity.com/paper/2604.05759/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 74 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Continuous-Time Flows for Efficient Inference and Density Estimation](https://mlsanity.com/paper/1709.01179/) (2017)
- [Active learning for structural reliability: survey, general framework and benchmark](https://mlsanity.com/paper/2106.01713/) (2021)
- [Conditional Variational Autoencoder for Learned Image Reconstruction](https://mlsanity.com/paper/2110.11681/) (2021)
- [Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions](https://mlsanity.com/paper/1911.09067/) (2019)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [Learning Conditional Variational Autoencoders with Missing Covariates](https://mlsanity.com/paper/2203.01218/) (2022)
- [Seismic fragility analysis using stochastic polynomial chaos expansions](https://mlsanity.com/paper/2208.07747/) (2022)
- [Surrogate modeling with functional nonlinear autoregressive models (F-NARX)](https://mlsanity.com/paper/2410.07293/) (2024)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)
- [A two-level Kriging-based approach with active learning for solving time-variant risk optimization problems](https://mlsanity.com/paper/2007.03942/) (2020)
- [Reliability analysis for non-deterministic limit-states using stochastic emulators](https://mlsanity.com/paper/2412.13731/) (2024)
- [mNARX+: A surrogate model for complex dynamical systems using manifold-NARX and automatic feature selection](https://mlsanity.com/paper/2507.13301/) (2025)
- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)

## Built on by (most cited first, 1 of 1)

- [Stochastic Emulation using Generalized Stratified Sampling for Performance-Based Risk Optimization of Structures](https://mlsanity.com/paper/2608.05006/) (2026)

## Abstract (arXiv)

Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem and remains computationally demanding, especially in high dimensions. This paper proposes a new RBDO framework based on a stochastic simulator viewpoint, in which the deterministic limit-state function and uncertain model inputs are combined into a unified stochastic representation. For a given design, the system response is characterized directly through its conditional output distribution rather than through an explicit limit-state function. Stochastic emulators are constructed in the design space to approximate this conditional distribution, enabling semi-analytical evaluation of failure probabilities or associated quantiles without Monte Carlo simulation. Two approaches are considered: generalized lambda models (GLaM) and stochastic polynomial chaos expansions (SPCE). Both yield deterministic mappings between design variables and reliability constraints, thereby eliminating the classical double-loop structure and enabling standard deterministic optimization. The approach is assessed on benchmark problems ranging from low to very high dimension, including stochastic excitation, and compared with Kriging in the full input space and heteroscedastic Gaussian processes in the design space. The proposed method provides substantial computational gains, particularly for high-dimensional random inputs, while retaining comparable efficiency to Kriging in low dimensions. Unlike heteroscedastic Gaussian processes, GLaM and SPCE also avoid restrictive assumptions on the conditional response distribution.