Neural Inverse Source Problem

Youngsun Wi, Jayjun Lee, Miquel Oller, Nima Fazeli
Proceedings of The 8th Conference on Robot Learning, PMLR 270:4371-4391, 2025.

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) 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v270-wi25a, title = {Neural Inverse Source Problem}, author = {Wi, Youngsun and Lee, Jayjun and Oller, Miquel and Fazeli, Nima}, booktitle = {Proceedings of The 8th Conference on Robot Learning}, pages = {4371--4391}, year = {2025}, editor = {Agrawal, Pulkit and Kroemer, Oliver and Burgard, Wolfram}, volume = {270}, series = {Proceedings of Machine Learning Research}, month = {06--09 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v270/main/assets/wi25a/wi25a.pdf}, url = {https://proceedings.mlr.press/v270/wi25a.html}, 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) 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.} }
Endnote
%0 Conference Paper %T Neural Inverse Source Problem %A Youngsun Wi %A Jayjun Lee %A Miquel Oller %A Nima Fazeli %B Proceedings of The 8th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2025 %E Pulkit Agrawal %E Oliver Kroemer %E Wolfram Burgard %F pmlr-v270-wi25a %I PMLR %P 4371--4391 %U https://proceedings.mlr.press/v270/wi25a.html %V 270 %X 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) 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.
APA
Wi, Y., Lee, J., Oller, M. & Fazeli, N.. (2025). Neural Inverse Source Problem. Proceedings of The 8th Conference on Robot Learning, in Proceedings of Machine Learning Research 270:4371-4391 Available from https://proceedings.mlr.press/v270/wi25a.html.

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