# REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis

arXiv: https://arxiv.org/abs/2606.13245 · HTML: https://mlsanity.com/paper/2606.13245/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling](https://mlsanity.com/paper/2310.15788/) (2023)
- [Contour location via entropy reduction leveraging multiple information sources](https://mlsanity.com/paper/1805.07489/) (2018)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes](https://mlsanity.com/paper/2308.04420/) (2023)
- [Lookahead Acquisition Functions for Finite-Horizon Time-Dependent Bayesian Optimization and Application to Quantum Optimal Control](https://mlsanity.com/paper/2105.09824/) (2021)
- [Multiobjective Aerodynamic Design Optimization of the NASA Common Research Model](https://mlsanity.com/paper/2507.10488/) (2025)
- [Two-stage Design for Failure Probability Estimation with Gaussian Process Surrogates](https://mlsanity.com/paper/2410.04496/) (2024)

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

- [A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification](https://mlsanity.com/paper/2606.28871/) (2026)

## Abstract (arXiv)

Multidisciplinary design analysis of coupled engineering systems requires the computation of equilibrium states in which all disciplinary coupling variables are mutually consistent. Conventional fixed-point iteration resolves this consistency problem separately at each design point, which can become expensive when disciplinary evaluations are costly and many analyses are required in outer-loop tasks such as multidisciplinary design optimization, uncertainty quantification, or digital twin updating. This paper introduces REMAL, a residual manifold surrogate modeling framework for coupled systems. Instead of approximating each discipline independently or directly learning converged coupling variables, the proposed method learns a surrogate model of the joint residual manifold via multitask Gaussian process models. An entropy-based active learning strategy selects additional residual evaluations near uncertain zero-contour regions, and equilibrium states for new design inputs are recovered by solving a nonlinear least squares optimization problem using only the trained surrogate. The method is evaluated on four engineering coupled system benchmarks: a satellite model, an aerostructural model, a finite-element gas-turbine heat-transfer and economics model, and a modified turbine model with added feedback coupling. Across these cases, REMAL consistently demonstrates the cost effectiveness when repeated evaluations of the fixed point across the design space are necessary. Theoretically, we show that, under mild assumptions, REMAL's predictive fixed point error is bounded.