Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress–strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.

Vitrimers represent an emerging class of sustainable polymers with self-healing capabilities enabled by dynamic covalent adaptive networks. However, their limited molecular diversity constrains their property space and potential applications. Recent developments in machine learning (ML) techniques accelerate polymer design by predicting properties and virtually screening candidates, yet the scarcity of available experimental vitrimer data poses challenges in training ML models. To address this, we leverage molecular dynamics (MD) data generated by our previous work to train and benchmark seven ML models covering six feature representations for glass transition temperature (Tg) prediction. By averaging predicted Tg from different models, the model ensemble approach outperforms individual models, allowing for accurate and efficient property prediction on unlabeled datasets. Two novel vitrimers are identified and synthesized, exhibiting experimentally validated higher Tg than existing bifunctional transesterification vitrimers, along with demonstrated healability. This work explores the possibility of using MD data to train ML models in the absence of sufficient experimental data, enabling the discovery of novel, synthesizable polymer chemistries with a wide range of desirable properties. The integrated MD–ML approach offers polymer chemists an efficient tool for accurate property prediction and designing polymers tailored to diverse applications.

The thermal conductivity of covalent organic frameworks (COFs), an emerging class of nanoporous polymeric materials, is crucial for many applications, yet the link between their structure and thermal properties remains poorly understood. Analysis of a dataset containing over 2400 COFs reveals that conventional features such as density, pore size, void fraction, and surface area do not reliably predict thermal conductivity. To address this, an attention-based machine learning model was trained, accurately predicting thermal conductivities even for structures outside the training set. The attention mechanism was then utilized to investigate the model's success. The analysis identified dangling molecular branches as a key predictor of thermal conductivity, leading us to define the dangling mass ratio (DMR), a descriptor that quantifies the fraction of atomic mass in dangling branches relative to the total COF mass. Feature importance assessments on regression models confirm the significance of DMR in predicting thermal conductivity. These findings indicate that COFs with dangling functional groups exhibit lower thermal transfer capabilities. Molecular dynamics simulations support this observation, revealing significant mismatches in the vibrational density of states due to the presence of dangling branches.

Mechanical metamaterials have garnered significant attention in materials and mechanics due to their unique geometric designs and tunable properties. However, metamaterials that allow for simultaneous multi-parameter control remain relatively scarce. This study introduces a multifunctional mechanical metamaterial where density, Young’s modulus, Poisson’s ratio, and thermal expansion coefficient are coordinately tunable through a combination of geometric design and material distribution. The influence of geometric and material parameters on the effective properties of the proposed metamaterial was systematically investigated through analytical solution, finite element simulation and experimental measurement. The results demonstrate that adjusting geometric parameters enables the structure to achieve a combination of lightweight characteristics, high adaptability, and negative Poisson’s ratio. Furthermore, the introduction of heterogeneous materials, leveraging the thermal strain mismatch at their interfaces, allows for simultaneous control over the structure’s thermal deformation, enabling either negative or positive thermal expansion. These combined properties are difficult to achieve with existing natural or artificial materials. This work can provide potential applications in flexible devices, smart structures, and thermal management.

Smooth and curved microstructural topologies found in nature—from soap films to trabecular bone—have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far are ad hoc, raising the challenge: how to systematically and efficiently inverse design such artificial microstructures with targeted topological features? Herein, surface curvature is explored as a design modality and a deep learning framework is presented to produce topologies with as-desired curvature profiles. The inverse design framework can generalize to diverse topological features such as tubular, membranous, and particulate features. Moreover, successful generalization beyond both the design and data space is demonstrated by inverse designing topologies that mimic the curvature profile of trabecular bone, spinodoid topologies, and periodic nodal surfaces for application in bio-scaffolds and implants. Lastly, curvature and mechanics are bridged by showing how topological curvature can be designed to promote mechanically beneficial stretching-dominated deformation over bending-dominated deformation.