arXiv:2507.10368cs.LGphysics.geo-ph2025-07被引 1

改进DeepONet架构,实现土力学固结问题的高效建模与加速求解。

Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variants

  • 将固结系数置于支路网络,提升模型对复杂变化的适应性
  • 新模型在1D下提速1.5-100倍,3D下达1000倍,显著提升计算效率
  • 适用于需要快速模拟和不确定性分析的岩土工程场景

深度算子网络(DeepONet)作为学习偏微分方程系统解算子的强大代理建模框架,正逐步拓展至工程领域,但在岩土工程中应用仍有限。本研究系统评估了多种DeepONet架构在固结问题中的表现。初始对比三种结构:标准架构(模型1、2),将固结系数嵌入支路网络;物理启发式架构(模型3),将系数置于主干网络。结果表明,模型3优于标准配置,但对过度孔隙压力剧烈变化的情形仍存局限。为此,提出基于主干网络傅里叶特征增强的DeepONet(模型4),有效捕捉快速变化函数。进一步将其扩展至3D场景。1D下计算速度提升1.5-100倍,3D下可达约1000倍。借助此效率,实现了3D固结问题不确定性量化的概念演示。研究表明,DeepONet在岩土工程中具备高效、通用的代理建模潜力,推动科学机器学习在该领域的早期融合。

原文摘要 · Abstract (English)

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical engineering remain limited. This study systematically evaluates several DeepONet architectures for the consolidation problem. We initially consider three architectures: a standard DeepONet with the coefficient of consolidation embedded in the branch net (Models 1 and 2), and a physics-inspired architecture with the coefficient embedded in the trunk net (Model 3). Results show that Model 3 outperforms the standard configurations (Models 1 and 2) but still has limitations when the target solution (excess pore pressures) exhibits significant variation. To overcome this limitation, we propose a Trunknet Fourier feature-enhanced DeepONet (Model 4) that addresses the identified limitations by capturing rapidly varying functions. We further extend Model 4 to 3D scenarios. Although the computational speedup can be modest in the 1D case (1.5-100x compared with traditional solvers), the speedup becomes more pronounced in 3D, reaching approximately 1,000x. Leveraging this efficiency, we offer a conceptual demonstration of DeepONet's potential to accelerate uncertainty quantification in a 3D consolidation problem. Overall, the study highlights the potential of DeepONets to enable efficient, generalizable surrogate modeling in geotechnical applications, advancing the integration of scientific machine learning in geotechnics, which is at an early stage.

DeepONet固结建模算子学习岩土工程

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