Fabio Amaral | Searcharxiv

arXiv2026

Robust Sparse Identification of Nonlinear Dynamics via Least Trimmed Squares

In this work, we propose a robust Sparse Identification of Nonlinear Dynamics (SINDy) pipeline for handling datasets corrupted by noise and outliers. The method decouples outlier filtering from sparse regression by combining Iterative Least Trimmed Squares (ILTS) with Sequentially Thresholded Least Squares (STLS). Unlike standard approaches that treat all observations uniformly within a single regression stage, the proposed ILTS-SINDy framework first applies an ILTS procedure that iteratively minimizes the sum of the smallest squared residuals to identify the most reliable observations without prior knowledge of outliers, after which STLS is used to recover a parsimonious governing model. Extensive numerical experiments show that ILTS-SINDy can significantly outperform existing robust SINDy variants across a range of outlier contamination levels, with performance maintained even under settings with up to $20\%$ corrupted observations.

math.OC↗

arXiv2024

Machine Learning in Viscoelastic Fluids via Energy-Based Kernel Embedding

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce a kernel function corresponding to a given viscoelastic stress model that implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) whose squared norm equals the total mechanical energy. Working implicitly with lifted representations in the RKHS via the kernel function provides natural and unambiguous metrics for distances and angles between flowfields without the need for hyperparameter tuning. Additionally, we present a solution to the preimage problem for our kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of our kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using our kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.

physics.flu-dyn↗