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This research advances computational efficiency for high-dimensional spatio-temporal systems by integrating adaptive sampling with dimensionality reduction in surrogate modeling. The method minimizes reliance on expensive physics-based simulations, which is critical for scaling uncertainty quantification and optimization tasks in complex multi-physics environments like gas turbine analysis. By balancing exploration and exploitation within a low-latent space, the approach offers a practical pathway to accelerate engineering workflows without sacrificing accuracy.
Adaptive surrogate modeling for high-dimensional spatio-temporal output
arXiv:2608.17250v1 Announce Type: cross Abstract: This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.
Abstract:This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.
Computational Engineering, Finance, and Science (cs.CE); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2608.17250 [cs.CE]
(or arXiv:2608.17250v1 [cs.CE] for this version)
https://doi.org/10.48550/arXiv.2608.17250 arXiv-issued DOI via DataCite (pending registration)
Struct. Multidiscip. Optim. 65, 290 (2022)
https://doi.org/10.1007/s00158-022-03402-x DOI(s) linking to related resources
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