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Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics‐informed deep‐learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the “eggshell” effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond.

Elastography is an imaging technique to reconstruct elasticity distributions of heterogeneous objects. Since cancerous tissues are stiffer than healthy ones, for decades, elastography has been applied to medical imaging for noninvasive cancer diagnosis. Although the conventional strain-based elastography has been deployed on ultrasound diagnostic-imaging devices, the results are prone to inaccuracies. Model-based elastography, which reconstructs elasticity distributions by solving an inverse problem in elasticity, may provide more accurate results but is often unreliable in practice due to the ill-posed nature of the inverse problem. We introduce ElastNet, a de novo elastography method combining the theory of elasticity with a deep-learning approach. With prior knowledge from the laws of physics, ElastNet can escape the performance ceiling imposed by labeled data. ElastNet uses backpropagation to learn the hidden elasticity of objects, resulting in rapid and accurate predictions. We show that ElastNet is robust when dealing with noisy or missing measurements. Moreover, it can learn probable elasticity distributions for areas even without measurements and generate elasticity images of arbitrary resolution. When both strain and elasticity distributions are given, the hidden physics in elasticity—the conditions for equilibrium—can be learned by ElastNet.

In recent years, machine learning (ML) techniques are seen to be promising tools to discover and design novel materials. However, the lack of robust inverse design approaches to identify promising candidate materials without exploring the entire design space causes a fundamental bottleneck. A general‐purpose inverse design approach is presented using generative inverse design networks. This ML‐based inverse design approach uses backpropagation to calculate the analytical gradients of an objective function with respect to design variables. This inverse design approach is capable of overcoming local minima traps by using backpropagation to provide rapid calculations of gradient information and running millions of optimizations with different initial values. Furthermore, an active learning strategy is adopted in the inverse design approach to improve the performance of candidate materials and reduce the amount of training data needed to do so. Compared to passive learning, the active learning strategy is capable of generating better designs and reducing the amount of training data by at least an order‐of‐magnitude in the case study on composite materials. The inverse design approach is compared with conventional gradient‐based topology optimization and gradient‐free genetic algorithms and the pros and cons of each method are discussed when applied to materials discovery and design problems.