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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Machine learning methods for forward and inverse PDEs
正反向 偏微分方程 机器学习
2023/4/27
本报告介绍我们近期的两项工作。(1) 求解PDE的PINN方法在处理时间发展方程时往往遇到难以收敛的困难。我们发展了时间方向的预训练PINN方法及自适应步长方法，解决了收敛性困难，使PDE求解精度能够得到系统性提高。我们在一系列时间发展方程上获得了比文献报道更精确的训练结果。(2) 辐射调源问题是一个典型的反问题，要求调整辐射输运方程的边条件(源)，使解满足特定设计目标。我们针对辐射输运方程的时序...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep learning of multi-scale PDEs based on data generated from particle methods
粒子方法 数据 多尺度 偏微分方程 深度学习
2023/4/26
Solving multi-scale PDEs is difficult in high-dimensional and/or convection-dominant cases. The interacting particle methods (IPM) are shown to outperform solving PDEs directly. Examples include compu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs
HT-Net 分层变压器 多尺度 偏微分方程 算子学习模型
2023/5/6
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...