4 papers
RUNNs: Ritz-Uzawa Neural Networks for Solving Variational Problems
Pablo Herrera, Jamie M. Taylor, Carlos Uriarte +3
Solving Partial Differential Equations (PDEs) using neural networks presents different challenges, including integration errors and spectral bias, often leading to poor approximati…
Consensus as cooling: a granular gas model for continuous opinions on structured networks
Carlos Uriarte, Pablo Rodriguez-Lopez, Nagi Khalil
A continuous-opinion model accounting for the social compromise propensity is theoretically and numerically analysed. An agent's opinion is represented by a real number that can be…
Solving Partial Differential Equations Using Artificial Neural Networks
Carlos Uriarte
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of…
Collocation-based Robust Variational Physics-Informed Neural Networks (CRVPINN)
Marcin ÅoÅ, Tomasz SÅużalec, PaweÅ Maczuga +3
Physics-Informed Neural Networks (PINNs) have been successfully applied to solve Partial Differential Equations (PDEs). Their loss function is founded on a strong residual minimiza…