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Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed. 

Abstract In this paper, we propose and compare two novel deep generative model-based approaches for the design representation, reconstruction, and generation of porous metamaterials characterized by complex and fully connected solid and pore networks. A highly diverse porous metamaterial database is curated, with each sample represented by solid and pore phase graphs and a voxel image. All metamaterial samples adhere to the requirement of complete connectivity in both pore and solid phases. The first approach employs a Dual Decoder Variational Graph Autoencoder to generate both solid phase and pore phase graphs. The second approach employs a Variational Graph Autoencoder for reconstructing/generating the nodes in the solid phase and pore phase graphs and a Transformer-based Large Language Model (LLM) for reconstructing/generating the connections, i.e., the edges among the nodes. A comparative study is conducted, and we found that both approaches achieved high accuracy in reconstructing node features, while the LLM exhibited superior performance in reconstructing edge features. Reconstruction accuracy is also validated by voxel-to-voxel comparison between the reconstructions and the original images in the test set. Additionally, discussions on the advantages and limitations of using LLMs in metamaterial design generation, along with the rationale behind their utilization, are provided. 

Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful proof paths, faces a discrepancy at the inference stage, as it must sample and try various tactics at each proof state until finding success, unlike its training which does not incorporate learning from failed attempts. Intuitively, a tactic that leads to a failed search path would indicate that similar tactics should receive less attention during the following trials. In this paper, we demonstrate the benefit of training models that additionally learn from failed search paths. Facing the lack of such trial-and-error data in existing open-source theorem-proving datasets, we curate a dataset on intuitionistic propositional logic theorems and formalize it in Lean, such that we can reliably check the correctness of proofs. We compare our model trained on relatively short trial-and-error information (TRIALMASTER) with models trained only on the correct paths and discover that the former solves more unseen theorems with lower trial searches. 

Abstract This paper investigates the midlatitude ionospheric disturbances over the American/Atlantic longitude sector during an intense geomagnetic storm on 23 April 2023. The study utilized a combination of ground‐based observations (Global Navigation Satellite System total electron content and ionosonde) along with measurements from multiple satellite missions (GOLD, Swarm, Defense Meteorological Satellite Program, and TIMED/GUVI) to analyze storm‐time electrodynamics and neutral dynamics. We found that the storm main phase was characterized by distinct midlatitude ionospheric density gradient structures as follows: (a) In the European‐Atlantic longitude sector, a significant midlatitude bubble‐like ionospheric super‐depletion structure (BLISS) was observed after sunset. This BLISS appeared as a low‐density channel extending poleward/westward and reached ∼40° geomagnetic latitude, corresponding to an APEX height of ∼5,000 km. (b) Coincident with the BLISS, a dynamic storm‐enhanced density plume rapidly formed and decayed at local afternoon in the North American sector, with the plume intensity being doubled and halved in just a few hours. (c) The simultaneous occurrence of these strong yet opposite midlatitude gradient structures could be mainly attributed to common key drivers of prompt penetration electric fields and subauroral polarization stream electric fields. This shed light on the important role of storm‐time electrodynamic processes in shaping global ionospheric disturbances.