Defesa de Dissertação de Mestrado do aluno Matheus Kerber.
Título da dissertação: Fast and Accurate Simulation of Deformable Solid Dynamics on Coarse Meshes
Resumo: This thesis introduces a novel hybrid simulator that combines a numerical Finite Element (FE) Partial Differential Equation solver with a Message Passing Neural Network (MPNN) to perform simulations of deformable solid dynamics on coarse meshes. Our work aims to provide accurate simulations with an error comparable to that obtained with more refined meshes in FE discretizations while maintaining computational efficiency by using an MPNN component that corrects the numerical errors associated with using a coarse mesh. We evaluate our model focusing on accuracy, generalization capacity, and computational speed compared to a reference numerical solver that uses 64 times more refined meshes. We introduce a new dataset for this comparison, encompassing three numerical benchmark cases: (i) free deformation after an initial impulse, (ii) stretching, and (iii) torsion of deformable solids. Based on simulation results, the study thoroughly discusses our methods strengths and weaknesses. The study shows that our method corrects an average of 95.9% of the numerical error associated with discretization while being up to 88 times faster than the reference solver. On top of that, our model is fully differentiable and can be embedded into a neural network layer, allowing it to be easily extended by future work. Our contributions also include demonstrating that our method achieves better results in learning and generalization capacity when compared to a purely data-oriented baseline simulator. Data and code are made available on <github link> for further investigations
Orientador: Prof. Dr. Waldemar Celes Filho
Banca: Prof. Dr. Jose Alberto Rodrigues Pereira Sardinha | Prof. Dr. Ivan Fabio Mota de Menezes | Prof. Dr. Leonardo Seperuelo Duarte
Assista a defesa pelo link: https://puc-rio.zoom.us/j/92665440011?pwd=UnNTR3RwcUNFd1hpVUVoUDJKODdodz09#success