DADD-PINN: Dual Adaptive Domain Decomposition Physics-Informed Neural Networks

When solving partial differential equations (PDEs), traditional Physics-Informed Neural Networks (PINNs) often encounter difficulties in capturing critical physical features and addressing information bias between subdomains. To overcome these limitations, this paper proposes a Dual Adaptive Domain Decomposition Physics-Informed Neural Network (DADD-PINN). The core of this method lies in the construction of a dual-driven architecture that facilitates intra-subdomain feature extraction and inter-subdomain feature coordination. Within each subdomain, the solver’s precision is significantly enhanced by integrating a multi-criterion adaptive sampling strategy with a dynamic weighting mechanism. Experimental results demonstrate that DADD-PINN reduces the optimal L2 error by 1–2 orders of magnitude compared to existing baselines. The model exhibits superior generalization and robustness across various physical fields, offering a new route toward accurate and efficient solutions for complex PDEs.

Authors

Institutions

Publication Details

Journal
Mathematics
Published
2026-02-23
DOI
https://doi.org/10.3390/math14040744
Primary Topic
Model Reduction and Neural Networks
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

DADD-PINN: Dual Adaptive Domain Decomposition Physics-Informed Neural Networks

Zhiying Ma, Yaxin Peng, Yunkang Xiong, Hongyu Wei et al.
Mathematics
Model Reduction and Neural Networks
article

DADD-PINN: Dual Adaptive Domain Decomposition Physics-Informed Neural Networks

Zhiying Ma, Yaxin Peng, Yunkang Xiong, Hongyu Wei, Zhihong Ding
article en

Abstract

When solving partial differential equations (PDEs), traditional Physics-Informed Neural Networks (PINNs) often encounter difficulties in capturing critical physical features and addressing information bias between subdomains. To overcome these limitations, this paper proposes a Dual Adaptive Domain Decomposition Physics-Informed Neural Network (DADD-PINN). The core of this method lies in the construction of a dual-driven architecture that facilitates intra-subdomain feature extraction and inter-subdomain feature coordination. Within each subdomain, the solver’s precision is significantly enhanced by integrating a multi-criterion adaptive sampling strategy with a dynamic weighting mechanism. Experimental results demonstrate that DADD-PINN reduces the optimal L2 error by 1–2 orders of magnitude compared to existing baselines. The model exhibits superior generalization and robustness across various physical fields, offering a new route toward accurate and efficient solutions for complex PDEs.

MathematicsVol. 14(4)
Shanghai University (CN)
National Natural Science Foundation of China
Openalex Percentile: Top 45%
Model Reduction and Neural Networks
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.