Advances on intelligent algorithms for scientific computing: an overview

Abstract

The field of computer science has undergone rapid expansion due to the increasing interest in improving system performance. This has resulted in the emergence of advanced techniques, such as neural networks, intelligent systems, optimization algorithms, and optimization strategies. These innovations have created novel opportunities and challenges in various domains. This paper presents a thorough examination of three intelligent methods: neural networks, intelligent systems, and optimization algorithms and strategies. It discusses the fundamental principles and techniques employed in these fields, as well as the recent advancements and future prospects. Additionally, this paper analyzes the advantages and limitations of these intelligent approaches. Ultimately, it serves as a comprehensive summary and overview of these critical and rapidly evolving fields, offering an informative guide for novices and researchers interested in these areas.

HiDeS: a higher-order-derivative-supervised neural ordinary differential equation for multi-robot systems and opinion dynamics

“…Its strength lies in processing time-variant data and adaptively learning from it. This modeling flexibility renders NODEs great potential for the intricate nature of dynamic systems (Hua et al, 2023 ; Wang et al, 2023 ; Jin et al, 2024 ), enabling a more nuanced understanding of complex dynamic systems.…”

“…As a learnable model parameterized by θ ∈ R n , a standard neural ordinary differential equation (NODE) ẋ = φ θ (x, t) is particularly adept at representing complex and nonlinear dynamics (Chen et al, 2018;Liufu et al, 2024), where x ∈ R d is the state at time t, ẋ = dx/dt denotes the time derivative of x, and φ(x, t) is a vector field with φ ∈ (R d × R → R d ) being a function of x and t. Its strength lies in processing timevariant data and adaptively learning from it. This modeling flexibility renders NODEs great potential for the intricate nature of dynamic systems (Hua et al, 2023;Wang et al, 2023;Jin et al, 2024), enabling a more nuanced understanding of complex dynamic systems. Despite these strengths, the standard NODE encounters expressivity limitations, failing to model functions like NOT operations (Kidger, 2021;Xu et al, 2023).…”