PINN 与 Deep Ritz:像有限差分与有限元,但关键不在网格
从同一个 Poisson 方程推导强形式残差与变分能量,逐项说明 PINN、Deep Ritz 与有限差分、有限元之间的相似与差异。
从同一个 Poisson 方程推导强形式残差与变分能量,逐项说明 PINN、Deep Ritz 与有限差分、有限元之间的相似与差异。
一家做设备参数扫描的工程团队,要把同一套动力学模型在一万个初始条件下各算一遍。方程和参数都已经写进求解器,瓶颈是反复积分以及数据在CPU、GPU之间搬运。此时再收集轨迹、训练一个替代模型,未必划算:训练费用、长时间误差和外推失败都要算在总账上。10月14日发布的预印本《The Physics Is the Network: Fast, Training-Free Neural Emulation
CERN 计划把部分加速器控制系统从 CentOS Linux 迁移到 Debian。表面看,这是一项发行版替换;放在约 2200 台控制计算机和约 17000 台受控设备的规模下,它更接近一次基础设施再认证。加速器控制系统连接电源、磁体、真空、射频、束流诊断和安全相关设备,许多计算机还安装定制 PCI 或 PCIe 板卡。系统稳定不仅关系到办公效率,也关系到昂贵实验设施能否按计划运行。
PhysicsNeMo 提供神经算子、图网络、PINN、科学数据管线和分布式 GPU 组件,用于训练工业代理模型。本文梳理其技术栈、方法选择、数据与验证要求,并说明它与传统 CFD、FEA 和试验体系的合理分工。
MathWorks新发布的MATLAB Agentic Toolkit,本质上不是一个简单的“让AI会写MATLAB代码”的插件,而是一套把MATLAB能力、工程知识和AI代理工作流绑定起来的基础设施。它一边通过MATLAB MCP Core Server给AI代理接上可执行的MATLAB环境,一边通过skills把MATLAB工程师的最佳实践注入代理,让AI不只是“会写几行.m文件”,而是能以更接近真实工程团队的方式完成建模、测试、诊断、应用开发与工具箱调用。
Cartesian 把算法教材做成了可执行、可回放、可交互的学习软件。本文拆解其技术路线,并进一步讨论:这种模式是否适合数值分析与科学计算类教科书写作?答案是,极其适合,而且可能比数据结构教材更有潜力。
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V
Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending Joseph M. Powers Department of Aerospace and Mechanical Engineering University of Notre Dame ASME V&V 2020 V