A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling

Area of Science:

• Computational Science
• Applied Mathematics
• Physical Phenomena Modeling

Background:

• Deterministic models lack realism for complex systems with inherent variability.
• Stochastic frameworks enhance model predictions by incorporating parameter, load, and geometric variability.
• High-dimensional random inputs and non-smooth responses pose challenges for existing uncertainty propagation methods.

Purpose of the Study:

• To develop a novel adaptive algorithm for efficient uncertainty propagation.
• To handle arbitrarily distributed random inputs and non-smooth stochastic responses.
• To improve computational efficiency and facilitate adaptivity in stochastic modeling.

Main Methods:

• Generalization of a multi-resolution approach using binary tree-based refinements in the stochastic space.
• Partitioning the stochastic space into progressively refined elements along a single dimension.
• Utilizing expansion coefficients to encode information for solution refinement and adaptivity.

Main Results:

• The proposed method significantly improves computational efficiency for uncertainty propagation.
• It effectively handles arbitrarily distributed random inputs and non-smooth stochastic responses.
• Binary refinements prevent exponential growth in basis cardinality and reduce regression complexity for high-dimensional inputs.

Conclusions:

• The developed adaptive algorithm offers a computationally efficient and robust solution for uncertainty propagation.
• It enhances the realism of computational models by accurately capturing complex variability.
• The method shows strong performance in benchmarks and cardiovascular flow simulations.