arXiv Machine Learning By Atticus Rex, Elizabeth Qian, David Peterson

Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data

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arXiv:2603. 22050v2 Announce Type: replace-cross Abstract: Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data.

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arXiv Machine Learning
Aug 27

Multi-output Gaussian process prediction of physical fields under linear equality constraints

The paper tackles the challenge of predicting multiple high‑dimensional physical fields that must satisfy linear equality constraints, a common scenario in physics‑informed machine learning. It critiques the conventional approach of deducing one field from others, showing its sensitivity to arbitrary choices and its impact on accuracy and uncertainty. To address this, the authors introduce a symmetric framework that first applies a row‑wise PCA to preserve constraints in a latent space, then trains a linearly‑constrained multi‑output Gaussian process using a specially parametrized kernel, and validate the method on population dynamics and CFD problems involving Reynolds stress tensors.

By Mahamat Hamdan Nassouradine, Cl\'ement Gauchy, Pierre-Emmanuel Angeli, S\'ebastien da Veiga