Related papers: Comment on "Machine learning conservation laws fro…

We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…

We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data. The method is model-agnostic in that it does not require explicit knowledge of the underlying…

We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization…

Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on…

Conservation laws are considered to be fundamental laws of nature. It has broad applications in many fields, including physics, chemistry, biology, geology, and engineering. Solving the differential equations associated with conservation…

Machine Learning (ML) models have been shown to potentially leak sensitive information, thus raising privacy concerns in ML-driven applications. This inspired recent research on removing the influence of specific data samples from a trained…

For over two decades, detecting rare events has been a challenging task among researchers in the data mining and machine learning domain. Real-life problems inspire researchers to navigate and further improve data processing and algorithmic…

As the use of Lithium-ion batteries continues to grow, it becomes increasingly important to be able to predict their remaining useful life. This work aims to compare the relative performance of different machine learning algorithms, both…

Understanding the geometric properties of gradient descent dynamics is a key ingredient in deciphering the recent success of very large machine learning models. A striking observation is that trained over-parameterized models retain some…

Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…

In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…

Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…

Machine unlearning (MU) aims to eliminate information that has been learned from specific training data, namely forgetting data, from a pre-trained model. Currently, the mainstream of existing MU methods involves modifying the forgetting…

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…

The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…

In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…

Personal digital data is a critical asset, and governments worldwide have enforced laws and regulations to protect data privacy. Data users have been endowed with the right to be forgotten of their data. In the course of machine learning…

Machine Unlearning has emerged as a critical area in artificial intelligence, addressing the need to selectively remove learned data from machine learning models in response to data privacy regulations. This paper provides a comprehensive…

Magnet errors in storage rings significantly degrade beam performance, impacting the brightness and stability of the light source. Therefore, beam-based correction is crucial for the safe operation of machines and the stability of radiated…

This paper has been withdrawn by the author due to a crucial accuracy error in Fig. 5. For precise performance of ALBNN please refer to Yoon et al.'s work in the following article. Yoon, H., Park, C. S., Kim, J. S., & Baek, J. G. (2013).…