Using Deep Learning to Improve Multiscale Simulations
Modern machine learning, especially deep learning, has offered tremendous computational innovations in the simulation, design, and discovery of new materials. While deep learning-based approaches can provide better computational efficiency and accuracy compared to conventional approaches, their applicability in computational material sciences is limited by several robustness issues, resulting from, for instance, the numerical instability in the training due to the intrinsic heterogeneity of the media, the lack of generalizability due to a small dataset, etc. Professor Yulong Lu (Mathematics) is working on a project called “Towards Robust Deep Learning Methods for Multiscale Simulation in Heterogeneous Materials,” that aims to address these issues by developing robust deep learning-based computational methods for solving multiscale partial differential equations arising from the simulation of heterogeneous materials. This is achieved by developing stable physics-informed neural networks that can resolve the solutions in the fine-scale and designing novel generative model-based data augmentation approach for recovering high-fidelity data from low-fidelity data, which are further deployed for predicting the macroscopic constitutive laws of materials. It is anticipated that the methodology proposed in this research would provide valuable insights for improving the robustness and generalizability of deep learning models in the material industry.
This project recently received a DSI Small Seed Grant. The Seed Grant program is intended to promote, catalyze, accelerate, and advance U of M-based data science research so that U of M faculty and staff are well prepared to compete for longer term external funding opportunities.
The program was updated in Summer 2024 to include three focus areas: Foundational Data Sciences; Digital Health and Personalized Health Care Delivery; and Agriculture and the Environment. The types of awards are Rapid Response Grants and new types, Awards for DSI Faculty Fellowship and Data Sets (Data as an Asset).
This project falls under the Foundational Data Sciences focus area.
Image description: Left: Reconstructed solution of Allen-Cahn equation. Right: Reference solution.
