M21. Physics-Informed Neural Networks for Solving Forward and Inverse Problems

Tomographic reconstruction is one of the most well-known inverse problems. Despite tomography’s long history, the fundamental interest in it remains unbroken as novel theoretical developments fuel new applications in tomography and, conversely, novel technologies and applications demand an even deeper understanding of the mathematical theory.

In recent years, the use of neural networks for solving forward and inverse problems involving differential equations has become a highly active area of research. While now commonly referred to as physics-informed neural networks (PINNs), the underlying ideas can be traced back to early works from the 1990s. This line of research is part of the broader field of scientific machine learning, which combines methods from scientific computing and machine learning. PINNs are attractive because they provide a monolithic approach: the neural network itself serves as the ansatz space, while the solution process is formulated through gradient-based optimization. This makes them particularly appealing for parameter identification and inverse problems. At the same time, despite their conceptual simplicity, PINNs are sensitive to hyperparameter choices, and their training process remains challenging and not fully understood.

This mini-symposium brings together researchers presenting state-of-the-art developments in PINNs for both forward and inverse problems. In addition to showcasing recent progress, we also encourage contributions that critically investigate the methodology and its limitations.

Organizers: 
Alexander Heinlein, Delft University of Technology, Netherlands, This email address is being protected from spambots. You need JavaScript enabled to view it.
Cordula Reisch, Roskilde University, Denmark, This email address is being protected from spambots. You need JavaScript enabled to view it.

Invited Speakers:
Zeina AL MASRY, FEMTO-ST Institute and SUPMICROTECH-ENSMM, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
An interpretable methodology for model identification based on port Hamiltonian systems and neural networks

Ander Biguri, University of Cambridge, United Kingdom, This email address is being protected from spambots. You need JavaScript enabled to view it.
Various physics-driven learned tomographic reconstructions and the impact of the physics knowledge

Pascal Fernsel, University of Bremen, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
Physics-informed Neural Networks for ParameterIdentification Problems with Applications in Automated Damage Detection

Roel Hacking, Eindhoven University of Technology, Netherlands, This email address is being protected from spambots. You need JavaScript enabled to view it.
Physics-informed neural networks for inverse optical design

Matthias Höfler, Graz University, Austria, This email address is being protected from spambots. You need JavaScript enabled to view it.
On parameter identification with physics-informed neural networks in three-dimensional elasticity

Andreas Langer, Lund University, Sweden, This email address is being protected from spambots. You need JavaScript enabled to view it.
Why PINNs make sense but can still fail: A mathematical investigation

Luca Ratti, University of Bologna, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Variational and learned techniques for (multi-frequency) Electrical Impedance Tomography

Aravinth Ravi, Kansas State University, USA, This email address is being protected from spambots. You need JavaScript enabled to view it.
A spectral-based model-informed neural network for solving the inverse source and scattering problems

Roberta Tittarelli, Université Bourgogne-Franche-Comté, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
Adapted VPINN for model parameter identification of beam-like structures