Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials

Area of Science:

• Computational Material Science
• Machine Learning Applications
• Partial Differential Equations

Background:

• Traditional numerical methods for material structural design are computationally intensive.
• Gradient-based optimization requires specific derivations and initialization.
• Existing physics-informed neural networks (PINNs) struggle with discontinuities common in composite materials.

Purpose of the Study:

• To develop a physics-informed machine learning approach for modeling discontinuous digital materials.
• To overcome the continuity limitations of standard PINNs in structural mechanics.
• To accelerate material design exploration by integrating physics-informed loss with design objectives.

Main Methods:

• Replaced the partial differential equation (PDE) residual with a weak formulation in the physics-informed training process.
• Applied the method to model digital materials with extreme structural discontinuity.
• Integrated physics-informed loss directly with design objectives for interactive optimization.

Main Results:

• The proposed approach successfully models digital materials with extreme structural discontinuity.
• Physical accuracy is maintained in data-free material surrogate modeling.
• The direct optimization process is accelerated without the need for model pretraining.

Conclusions:

• The weak formulation in PINNs effectively handles structural discontinuities in material modeling.
• This data-free, accelerated optimization approach enhances material design exploration.
• The method offers a promising alternative for complex composite material simulations.