← back

Evolving Collocation Sampling for Stochastic Minimization

with Akshay J. Thomas, Eduardo Barocio, and Ilias Bilionis · SAMPE Conference 2025 · PDF

PINNs use automatic differentiation to compute derivatives of the solution with respect to space and time, which allows flexible sampling in the domain. Flexible sampling refers to the ability to select points dynamically from spatial and temporal domain during training, without being constrained by a fixed mesh or grid structure, as is typical in FEM. This feature allows PINNs to adaptively sample regions of interest within the domain, such as areas with sharp gradients or rapidly evolving features. These sampling points are called collocation points.

Workflow
Workflow
Multilayer architecture
Multilayer architecture
Layerwise sampling
Layerwise sampling
Collocation point sampling
Collocation point sampling
Discussion
Discussion