Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

Area of Science:

• Computational Science
• Applied Mathematics
• Machine Learning

Background:

• Multiscale modeling is crucial for multiphysics systems with disparate scales, but high-fidelity simulations are computationally expensive.
• Existing methods struggle with the high cost of detailed simulations, especially for time-dependent problems.
• Bridging different model resolutions (e.g., continuum and particle methods) presents significant computational challenges.

Purpose of the Study:

• To develop an efficient multiscale modeling framework using machine learning to reduce computational costs.
• To employ DeepONet, a neural operator, as a surrogate for expensive high-fidelity solvers.
• To demonstrate the framework's ability to accurately predict system responses under new conditions.

Main Methods:

• Trained DeepONet offline on data from a fine-resolution solver to learn fine-scale dynamics.
• Coupled the trained DeepONet with standard PDE solvers for real-time prediction.
• Validated the approach using static and time-dependent benchmarks, including coupling finite element methods (FEM) with a neural operator surrogate for Smoothed Particle Hydrodynamics (SPH).

Main Results:

• The DeepONet-based multiscale modeling framework significantly reduces computational expense.
• DeepONet accurately captures fine-scale dynamics and generalizes well for new predictions.
• Demonstrated successful coupling of continuum (FEM) and particle-based (SPH surrogate) models for material response prediction.

Conclusions:

• Machine learning, specifically DeepONet, offers an efficient surrogate for high-fidelity solvers in multiscale modeling.
• The proposed framework enables cost-effective and accurate predictions for complex multiphysics problems.
• This approach facilitates the integration of diverse modeling techniques and interface conditions.