用分阶段学习提升物理神经网络长期模拟精度
Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks
- 将长期问题拆成短时子问题，逐步递进求解
- 在非线性波传播等任务中保持长期计算稳定
- 适合需要长时间高精度仿真的工程场景
本文提出一种基于课程迁移学习的物理信息神经网络（CTL-PINN），用于长期物理与力学行为模拟。核心创新在于将长期问题分解为一系列短期子问题：先用标准PINN求解首段，随后通过课程学习融合历史信息处理后续时间域问题，并引入迁移学习技术，有效利用前期训练数据解决序列时间域转移问题。该方法结合课程学习与迁移学习优势，克服了传统PINN易陷入局部最优、CL-PINN长期误差累积及TL-PINN计算效率低的问题。在非线性波传播、基尔霍夫板动力响应以及三峡库区水动力模型中的应用验证了其有效性与鲁棒性，展现出对长期计算挑战的强大应对能力。
原文摘要 · Abstract (English)
This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。