2 days ago · This work investigates in detail how irregular discretizations, design surface boundaries, and complex geometries can influence the progress of a gradient-based ...
6 days ago · Recently, machine learning techniques have been introduced to accelerate the process of solving PDEs by learning a neural operator as a mapping from variable ...
Nov 1, 2024 · Physics-informed neural network has emerged as a promising approach for solving partial differential equations. However, it is still a challenge for the ...
Oct 16, 2024 · A new numerical framework is developed to solve general nonlinear and nonlocal PDEs on complicated two-dimensional domains.
6 days ago · Our approach, utilizing a physics-constrained coupled neural differential equation (PCNDE) framework, demonstrates superior performance compared to conventional ...
Oct 16, 2024 · The goal of the workshop is to foster collaboration among all MFEM users and developers, share the latest MFEM features with the broader community.
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Oct 16, 2024 · This study proposes a Neural Network-augmented Differentiable Finite Element Method (NNDFEM) by combining PINN and finite element approximation.
Oct 17, 2024 · In this paper the topological derivative for an arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system ...
Oct 14, 2024 · In this talk, we will quantitatively examine the interaction between generic shock formation and viscous effects as the viscosity tends to zero.
Oct 17, 2024 · Evaluation of boundary conditions. For all optimization results, we compute gradients using multiple different boundary conditions. Since the boundary ...