Problem
Research questions and friction points this paper is trying to address.
multifidelity
triangular transport maps
high-fidelity data scarcity
distribution mapping
Multifidelity Formulations for Triangular Transport
🤖 AI Summary
This study addresses the challenge of constructing triangular transport maps due to the scarcity of high-fidelity data. To overcome this limitation, we propose a multi-fidelity approximation framework that establishes a bijective mapping from a reference density to the high-fidelity target distribution. The core innovation lies in designing two strategies—hierarchical composition and non-hierarchical monotonic correction—that effectively integrate low-fidelity information to enhance mapping estimation accuracy. Experimental results demonstrate that the proposed approach significantly improves the quality of map construction under limited high-fidelity samples. Furthermore, it effectively enhances performance in downstream tasks, including conditional sampling and uncertainty quantification.
📝 Abstract
We develop multifidelity methods for constructing triangular transport maps from samples, when high-fidelity data are scarce but lower-fidelity data are more abundant. Using this set of multifidelity data, we approximate a triangular transport map that bijectively maps between a tractable reference density and the high-fidelity target distribution. We introduce two strategies to leverage low-fidelity data: a hierarchical approach that composes maps between adjacent fidelity levels, and a non-hierarchical method that incorporates low-fidelity information through monotonicity-preserving corrections to the map parameterization. Numerical experiments compare these strategies with single-fidelity transport and demonstrate how the proposed multifidelity approaches can improve map estimation from limited high-fidelity data. To illustrate the broader utility of the learned maps, we also deploy them in a downstream amortized simulation-based inference task. This example shows that multifidelity improvements in map estimation can translate to improved conditional sampling and uncertainty quantification when high-fidelity data are scarce.
Innovation
Methods, ideas, or system contributions that make the work stand out.
multifidelity methods
triangular transport maps
hierarchical approach
monotonicity-preserving corrections
simulation-based inference
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