Local gradient neural operator predicts evolving mechanical systems well
Local gradient neural operator
Machine Learning
Summary
Predicting how things like heat or fluids will change over time usually needs deep understanding of complicated math equations. The researchers introduce a new method called the local gradient neural operator, which learns from data in a simpler, more understandable way. Their approach uses local patterns that mimic traditional numerical methods and keeps things efficient with fewer parameters. This method works well on many types of problems, including those involving diffusion, flow, and even quantum effects.
What this means in practice
- •For mechanical engineers: Predict how mechanical systems evolve over time from limited data by using a more interpretable and efficient neural method.
- •For quantum computing developers: Model quantum phenomena dynamics more efficiently by leveraging learned local kernels that reflect physical system symmetries.
Authors
Baiming Zhang, Jinsong Tang, Ying Xu, Lihua Chen, Shiying Xiong
Abstract
Field temporal prediction and source identification constitute canonical problems in dynamical systems. Conventional approaches to these problems depend on a thorough understanding of the governing partial differential equations (PDEs). Recently, deep learning, as represented by neural operators, has provided a data-driven paradigm for addressing such tasks. However, most existing global neural operators for PDEs require large training datasets and many learnable parameters, with limited interpretability and generalization. We propose the local gradient neural operator (LGNO) as a lightweight and interpretable alternative for field temporal evolution prediction and source identification in typical mechanical problems. The method builds on priors from nonlinear gradient discretization and uses multilayer perceptron convolutional layers to learn translation-invariant local kernels that resemble discrete stencils. A zero consistent stencil factorization separates coefficient learning from field reconstruction, rendering the learned operators more transparent. For problems with symmetries, network folding shares equivalent components and reduces parameter counts. We evaluate the method on PDE benchmarks covering linear and nonlinear, static and dynamic, and low and high dimensional cases. Results show that LGNO maintains accuracy, parameter efficiency, and rollout stability across these tasks, and further exhibits wide applicability to mechanical problems including diffusion, flow, and quantum phenomena.