Work

Parameter estimation and adaptive solution of the Leray-Burgers equation using physics-informed neural networks

Year: 2025

Type: article

Abstract: This study presents a unified framework that integrates physics-informed neural networks (PINNs) to address both the inverse and forward problems of the one-dimensional Leray-Burgers equation. First, we investigate the inverse problem by empirically determining a physically consistent range of the characteristic wavelength parameter α for which the Leray-Burgers solutions closely approximate those of the inviscid Burgers equation, using PINN-based computational experiments. Next, we solve the forward problem using a PINN architecture where α is dynamically optimized during training via a dedicated subnetwork, Alpha2Net. Crucially, Alpha2Net enforces α to remain within the inverse problem-derived bounds, ensuring physical fidelity while jointly optimizing network parameters (weights and biases). This integrated approach effectively captures complex dynamics, such as shock and rarefaction waves. This study also highlights the effectiveness and efficiency of the Leray-Burgers equation in real practical problems, specifically Traffic State Estimation.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100619

Authors: DooSeok Lee, Yuncherl Choi, Bong-Sik Kim

Institutions: Daegu Gyeongbuk Institute of Science and Technology, Kwangwoon University, American University of Ras Al Khaimah

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funders: National Research Foundation, Kwangwoon University, National Research Foundation of Korea, Ministry of Science and ICT, South Korea