Novel Loss Function Construction for Neural Network-Based Prediction of Complex High-Dimensional Nonlinear Dynamical Systems
Year: 2025
Type: article
Abstract: Traditional loss functions such as mean squared error (MSE) are widely employed, but they often struggle to capture the dynamic characteristics of high-dimensional nonlinear systems. To address this issue, we propose an improved loss function that integrates linear multistep methods, system-consistency constraints, and prediction-phase error control. This construction simultaneously improves training accuracy and long-term stability. Furthermore, the introduction of recursive loss and interpolation strategies brings the model closer to practical prediction scenarios, broadening its applicability. Numerical simulations demonstrate that this construction significantly outperforms both mean square error and existing custom loss functions in terms of performance.
Source: Informatica
DOI: 10.15388/25-infor607
Authors: Kun An, Ying Sun, Minghui Yao, Junhua Zhang
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415618605