Physics-informed UNets for discovering hidden elasticity in heterogeneous materials

Area of Science:

• Computational mechanics
• Biomedical engineering
• Machine learning for science

Background:

• Soft biological tissues exhibit complex mechanical behaviors due to heterogeneous structural components.
• Accurate characterization of tissue mechanics is crucial for understanding physiological processes and diagnosing diseases.
• Inverse problems in elasticity are computationally intensive and challenging for complex material distributions.

Purpose of the Study:

• To develop a novel UNet-based neural network model (El-UNet) for inferring spatial distributions of mechanical parameters in soft tissues.
• To compare the performance of El-UNet against traditional fully-connected physics-informed neural networks.
• To introduce and evaluate a self-adaptive spatial loss weighting approach for improved inversion accuracy.

Main Methods:

• Development of El-UNet, a convolutional neural network architecture adapted for elasticity inversion.
• Utilizing strain maps, boundary conditions, and domain physics as inputs for the neural network.
• Generation of synthetic data through finite-element simulations of heterogeneous isotropic domains.
• Characterization of different El-UNet variations and implementation of a self-adaptive spatial loss weighting strategy.

Main Results:

• El-UNet demonstrated superior accuracy and computational efficiency compared to fully-connected physics-informed neural networks for isotropic linear elasticity.
• The self-adaptive spatially weighted El-UNet models achieved the most accurate reconstructions within equal computation times.
• Learned spatial weighting distributions correlated with regions of inaccurate reconstruction in unweighted models, highlighting improved performance.

Conclusions:

• El-UNet provides a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks.
• The proposed self-adaptive spatial loss weighting enhances the accuracy of mechanical parameter reconstruction.
• This framework offers a promising, fast approach for challenging three-dimensional inverse elasticity problems in biological tissues.