Local gradient neural operator
Researchers propose LGNO, a lightweight interpretable neural operator using learnable local stencils, matching global-operator accuracy on PDE benchmarks with fewer parameters.
LGNO builds on nonlinear gradient discretization priors and uses multilayer perceptron convolutional layers to learn translation-invariant local kernels resembling discrete stencils. A zero consistent stencil factorization separates coefficient learning from field reconstruction, and network folding shares equivalent components to cut parameter counts for symmetric problems. Evaluations on linear and nonlinear, static and dynamic, and low- and high-dimensional PDE benchmarks show maintained accuracy, parameter efficiency, and rollout stability, with applicability to diffusion, flow, and quantum problems.
- Targets field temporal prediction and source identification without full knowledge of governing PDEs
- Learns translation-invariant local kernels resembling discrete stencils via MLP convolutional layers
- Network folding reduces parameters for problems with symmetries
- Evaluated across diffusion, flow, and quantum mechanical PDE benchmark tasks
- Tags
- dynamical-systemsinterpretabilityneural-operatorsparameter-efficiencypdescientific-machine-learning
- Products
- LGNO
From the original article
1 min read at arxiv.orgField 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.
By Baiming Zhang · arxiv.org
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