Data-driven mechanics with neural ordinary differential equations: from forward modeling to inverse material characterization

Characterizing the nonlinear, heterogeneous mechanical behavior of complex materials requires frameworks that balance data-driven flexibility with physical rigor. This seminar presents a unified approach using Neural Ordinary Differential Equations (NODEs) to construct polyconvex strain energy functions that satisfy essential thermodynamic and mathematical constraints by design. We extend this foundation into a generative regime using probabilistic diffusion fields to sample spatially correlated material properties and quantify uncertainty across populations. Finally, we integrate these models with hyper-networks to solve inverse problems, recovering full constitutive responses directly from full-field experimental data, such as Digital Image Correlation (DIC), without prescribing closed-form material laws. Validated with synthetic and experimental data from biological tissues and 3D-printed elastomers, this framework provides a robust, physics-consistent route for discovering the mechanics of arbitrary heterogeneous systems. Contatti: francesco.regazzoni@polimi.it stefano.pagani@polimi.it