Bi-fidelity Interpolative Decomposition for Multimodal Data

2025/09/10 by Murray Cutforth, Cutforth, Murray, Tiffany Fan +7 · 1 citation
Computer Science · #Anomaly Detection Techniques and Applications #Computational Physics and Python Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2509.12243

openalex publication_date 2025/09/10 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

Multi-fidelity simulation is a widely used strategy to reduce the computational cost of many-query numerical simulation tasks such as uncertainty quantification, design space exploration, and design optimization. The reduced basis approach based on bi-fidelity interpolative decomposition is one such approach, which identifies a reduced basis, along with an interpolation rule in that basis, from low-fidelity samples to approximate the corresponding high-fidelity samples. However, as illustrated in the present study, when the model response is multi-modal and mode occupancy is stochastic, the assumptions underpinning this approach may not hold, thus leading to inaccurate estimates. We introduce the multi-modal interpolative decomposition method using bi-fidelity data, an extension tailored for this use case. Our work is motivated by a complex engineering application: a laser-ignited methane-oxygen rocket combustor evaluated over uncertain input parameters, exhibiting a bifurcation-like phenomenon in some regions of parameter space. Unlike the standard bi-fidelity interpolative decomposition approach, the proposed method can approximate a dataset of high-fidelity simulations for 16% of the cost, while maintaining relatively high correlation (0.70--0.90) with parameter sensitivities.

Citations

• Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition
• Pre-classification based stochastic reduced-order model for time-dependent complex system
• Bi-fidelity Reduced Polynomial Chaos Expansion for Uncertainty Quantification
• Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey
• On transfer learning of neural networks using bi-fidelity data for uncertainty propagation
• A multi-fidelity neural network surrogate sampling method for\n uncertainty quantification
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
• Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence
• Survey of multifidelity methods in uncertainty propagation, inference,\n and optimization
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Multilevel Monte Carlo methods
• Recursive co-kriging model for Design of Computer experiments with multiple levels of fidelity with an application to hydrodynamic
• Predicting the output from a complex computer code when fast approximations are available
• GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS
• The Approximation of One Matrix by Another of Lower Rank

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