Neural Inverse Source Problems

TL;DR

This paper introduces a Physics-Informed Neural Network approach for solving inverse source problems in robotics, enabling joint source and state estimation from partial, noisy data with greater flexibility and fewer discretization constraints.

Contribution

It presents a novel PINN-based method that outperforms traditional techniques by integrating diverse constraints, avoiding complex discretizations, and handling real measurement gradients effectively.

Findings

Successfully applied to multiple simulation and real-world scenarios.

Able to handle high-order PDEs and complex boundary conditions.

Demonstrates robustness to noisy and partial observations.

Abstract

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.