Fully data-driven inverse characterization of heterogeneous materials with hyper-network neural ODEs

Accurately identifying the mechanical behavior of heterogeneous materials is a central challenge in materials science, with implications for the design of composites, metamaterials, and engineered biological tissue. Conventional inverse methods require closed-form constitutive models and are often restricted to simplified geometries or homogeneous properties, limiting their ability to capture complex, spatially varying material responses. Here, we introduce a fully data-driven framework for inverse characterization that recovers the complete constitutive behavior of heterogeneous solids directly from full-field displacement data, without prescribing a specific material law. Our approach combines neural ordinary differential equation (NODE) constitutive models, which inherently satisfy key thermodynamic and mathematical constraints, with a hyper-network that maps each material point to its local NODE, enabling continuous representation of arbitrary spatial variation in material properties. The loss function at the center of the method includes the strong form of equilibrium and traction boundary conditions. We demonstrate the method’s robustness on synthetic datasets, including heterogeneous isotropic and anisotropic materials, noise-contaminated measurements, and complex geometries, and validate it with digital image correlation experiments on 3D-printed elastomers. This framework provides a general, physically consistent route to inferring heterogeneous constitutive behavior from experimental data, offering new opportunities for accurate mechanical characterization across a broad range of material systems.