Coupled Input-Output Dimension Reduction for Uncertainty Quantification

Mots clé :

• Bayesian inference
• Global sensitivity analysis
• Optimal experimental design

The "curse of dimensionality" is a serious challenge across many fields of applied maths. It refers to the exponential growth of computational complexity with increasing dimensions, often rendering established algorithms ineffective or completely useless. Dimension reduction methods aim to "break the curse" by identifying underlying low-dimensional structures that are present in many physical systems.
Existing methods typically reduce a single space and are applied separately to the input and output space of high-dimensional problems.
However, choosing a lower-dimensional input subspace influences which output subspace is relevant and vice versa. 

We introduce a novel approach to jointly reduce both the input and output space of high-dimensional functions using gradient information. Our method is easy to implement, has guaranteed error bounds, and delivers interpretable low-dimensional structures, making it well-suited for real-world applications. We further establish its connection to global sensitivity analysis and Bayesian optimal experimental design, demonstrating how it can accelerate these notoriously computationally expensive tasks. 

Président:

Florence FORBES (Centre INRIA de l'Université de Grenoble)

Directeurs:

• Elise ARNAUD (Université Grenoble Alpes )
• Olivier ZAHM (Centre INRIA de l'Université de Grenoble )

Raporteurs:

• Omar GHATTAS (University of Texas Austin )
• Olivier ROUSTANT (INSA Toulouse )

Examinateurs:

• Ricardo BAPTISTA (California Institute of Technology )
• Guillaume PERRIN (Université Gustave Eiffel )