Document detail
ID
oai:arXiv.org:2407.10654
Topic
Mathematics - Numerical Analysis Physics - Computational PhysicsAuthor
Berardi, Marco Difonzo, Fabio Icardi, MatteoCategory
Computer Science
Year
2024
listing date
12/4/2024
Keywords
models parameters pinn inverseAbstract
Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations.
This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection-diffusion-reaction problems.
Once a suitable PINN is established to solve the forward problem, the transport parameters are added as trainable parameters.
We find that, for the inverse problem to converge to the correct solution, the different components of the loss function (data misfit, initial conditions, boundary conditions and residual of the transport equation) need to be weighted adaptively as a function of the training iteration (epoch).
Similarly, gradients of trainable parameters are scaled at each epoch accordingly.
Several examples are presented for different test cases to support our PINN architecture and its scalability and robustness.
Berardi, Marco,Difonzo, Fabio,Icardi, Matteo, 2024, Inverse Physics-Informed Neural Networks for transport models in porous materials
Assessing the Equivalence of Brain-Derived Measures from Two 3D T1-Weighted Acquisitions: One Covering the Brain and One Covering the Brain and Spinal Cord
>0 t1-weighted brain icc cns-t1 measures spinal
