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Inverse Elasticity Physics-Informed Neural Network (PINN)
#Machine Learning
#Physics-Informed Neural Networks
#Cauchy Momentum PDE
#Inverse Problems
#Sobol Collocation
#Continuum Mechanics
Formulated and implemented a physics-informed deep learning architecture to solve the ill-posed inverse elasticity problem of reconstructing spatially varying material properties from sparse experimental surface measurements.
Methodology & Mathematical Framework
- Direct Hybrid Collocation Architecture: Designed a deep neural network that represents displacement ((u, v)), stress ((\sigma_{xx}, \sigma_{yy}, \sigma_{xy})), strain ((\varepsilon)), and the spatially distributed Young’s modulus field ((E(x,y))) across 3 distinct Additively Manufactured (AM) lattice specimens.
- PDE-Constrained Multi-Objective Optimization:
- Embedded the governing 2D Cauchy Momentum balance equations ((\nabla \cdot \boldsymbol{\sigma} + \mathbf{b} = \mathbf{0})) directly into the neural network loss function using automatic differentiation.
- Formulated a 7-objective composite loss balancing boundary conditions, constitutive Hookean stress-strain relationships, and PDE residual compliance.
- Sparse Anchor Fusion & Sampling: Unified 8 Digital Image Correlation (DIC) experimental anchor measurement zones with 10,000+ Sobol low-discrepancy collocation points distributed across the domain interior to guide convergence without requiring destructive interior slicing.
- Results: Successfully reconstructed continuous modulus degradation gradients and identified local defect concentrations in 3D-printed meta-materials with high spatial fidelity.