用神经网络解决机器人中的源函数反问题，精度高且无需复杂网格
Neural Inverse Source Problems
- 基于物理约束的神经网络，联合估计未知源和系统状态
- 在含噪声观测下仍能准确重建4阶偏微分方程系统
- 适合需融合物理规律与实测数据的机器人感知任务
重建未知外部源函数是机器人领域（包括操作、飞行和水下机器人）中关键的感知能力。本文提出一种基于物理信息神经网络（PINN）的方法，用于求解机器人中的逆源问题，可在部分且含噪观测条件下联合识别未知源函数和系统的完整状态。相比传统方法（有限元法FEM和数据驱动方法），该方法具有更强的约束集成能力，无需复杂离散化（如网格划分），可直接融入真实测量梯度，且不依赖训练数据的多样性和质量。我们在三个仿真与真实场景中验证了该方法，涵盖最高4阶偏微分方程（PDEs）、Signorini与Dirichlet等边界条件，以及Chamfer距离和L2范数等多种回归损失。
原文摘要 · Abstract (English)
Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network (PINN [1]) based approach for solving the inverse source problems in robotics, jointly identifying unknown source functions and the complete state of a system given partial and noisy observations. Our approach demonstrates several advantages over prior works (Finite Element Methods (FEM) and data-driven approaches): it offers flexibility in integrating diverse constraints and boundary conditions; eliminates the need for complex discretizations (e.g., meshing); easily accommodates gradients from real measurements; and does not limit performance based on the diversity and quality of training data. We validate our method across three simulation and real-world scenarios involving up to 4th order partial differential equations (PDEs), constraints such as Signorini and Dirichlet, and various regression losses including Chamfer distance and L2 norm.
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