Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (L TI) systems on a single trajectory. Current state-of-the-art approaches require a sample complexity linear in n, the state dimension, which incurs a state norm that blows up exponentially in n. We propose a novel algorithm based on spectral decomposition that only needs to learn "a small part" of the dynamical matrix acting on its unstable subspace. We show that, under proper assumptions, our algorithm stabilizes an L TI system on a single trajectory with O ( k log n) samples, where k is the instability index of the system. This represents the first sub-linear sample complexity result for the stabilization of L TI systems under the regime when k = o (n).

Shenzhen JL Computational Science and Applied Research Institute, Shenzhen 518131, People's Republic of China (Dated: December 15, 2023) "AI for science" is widely recognized as a future trend in the development of scientific research. Currently, although machine learning algorithms have played a crucial role in scientific research with numerous successful cases, relatively few instances exist where AI assists researchers in uncovering the underlying physical mechanisms behind a certain phenomenon and subsequently using that mechanism to improve machine learning algorithms' efficiency. This article uses the investigation into the relationship between extreme Poisson's ratio values and the structure of amorphous networks as a case study to illustrate how machine learning methods can assist in revealing underlying physical mechanisms. Upon recognizing that the Poisson's ratio relies on the low-frequency vibrational modes of dynamical matrix, we can then employ a convolutional neural network, trained on the dynamical matrix instead of traditional image recognition, to predict the Poisson's ratio of amorphous networks with a much higher efficiency. Through this example, we aim to showcase the role that artificial intelligence can play in revealing fundamental physical mechanisms, which subsequently improves the machine learning algorithms significantly. Using artificial intelligence (AI) to help scientific research and design, reducing the reliance on extensive experimental has emerged as a prominent and well-recognized trial and error. Fueled by research generally encompasses the following three the vigorous advancements in computational science, machine stages: learning have experienced unprecedented growth in 1.