First Integral
First integrals, representing quantities conserved during a system's evolution, are a central concept in dynamical systems and related fields. Current research focuses on discovering and utilizing first integrals from data, employing methods like sparse regression (SINDy), neural networks (including neural differential equations), and integral projection-based autoencoders, often integrated with other techniques such as model predictive control or symbolic regression. These advancements enable more robust parameter estimation, improved model interpretability, and enhanced predictive capabilities across diverse applications, ranging from physics simulations and chemical process optimization to robotics and image analysis. The ability to efficiently learn and utilize first integrals promises significant improvements in modeling complex systems and solving challenging scientific problems.
Papers
Integrating Multi-Physics Simulations and Machine Learning to Define the Spatter Mechanism and Process Window in Laser Powder Bed Fusion
Olabode T. Ajenifujah, Francis Ogoke, Florian Wirth, Jack Beuth, Amir Barati Farimani
Integrating supervised and unsupervised learning approaches to unveil critical process inputs
Paris Papavasileiou, Dimitrios G. Giovanis, Gabriele Pozzetti, Martin Kathrein, Christoph Czettl, Ioannis G. Kevrekidis, Andreas G. Boudouvis, Stéphane P. A. Bordas, Eleni D. Koronaki
DualFocus: Integrating Plausible Descriptions in Text-based Person Re-identification
Yuchuan Deng, Zhanpeng Hu, Jiakun Han, Chuang Deng, Qijun Zhao