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The inception of physics-constrained or physics-informed machine learning represents a paradigm shift, addressing the challenges associated with data scarcity and enhancing model interpretability. This innovative approach incorporates the fundamental laws of physics as constraints, guiding the training process of machine learning models. In this work, the physics-constrained convolutional recurrent neural network is further extended for solving spatial-temporal partial differential equations with arbitrary boundary conditions. Two notable advancements are introduced: the implementation of boundary conditions as soft constraints through finite difference-based differentiation, and the establishment of an adaptive weighting mechanism for the optimal allocation of weights to various losses. These enhancements significantly augment the network's ability to manage intricate boundary conditions and expedite the training process. The efficacy of the proposed model is validated through its application to two-dimensional phase transition, fluid dynamics, and reaction-diffusion problems, which are pivotal in materials modeling. Compared to traditional physics-constrained neural networks, the physics-constrained convolutional recurrent neural network demonstrates a tenfold increase in prediction accuracy within a similar computational budget. Moreover, the model's exceptional performance in extrapolating solutions for the Burgers' equation underscores its utility. Therefore, this research establishes the physics-constrained recurrent neural network as a viable surrogate model for sophisticated spatial-temporal PDE systems, particularly beneficial in scenarios plagued by sparse and noisy datasets. 

Reconstructing 3D granular microstructures within volumes of arbitrary geometries from limited 2D image data is crucial for predicting the material properties, as well as performances of structural components accounting for material microstructural effects. We present a novel generative learning framework that enables exascale reconstruction of granular microstructures within complex 3D geometric volumes. Building upon existing transfer learning techniques using pre-trained convolutional neural networks (CNN), we introduce several key innovations to overcome the difficulties inherent in arbitrary geometries. Our framework incorporates periodic boundary conditions using circular padding techniques, ensuring continuity and representativeness of the reconstructed microstructures. We also introduce a novel seamless transition reconstruction (STR) method that creates statistically equivalent transition zones to integrate multiple pre-existing 3D microstructure volumes. Based on STR, we propose a cost-effective strategy for reconstructing microstructures within complex geometric volumes, minimizing computational waste. Validation through numerical experiments using kinetic Monte Carlo simulations demonstrates accurate reproduction of grain statistics, including grain size distributions and morphology. A case study involving the reconstruction of a 4-blade propeller microstructure illustrates the method’s capability to efficiently handle complex geometries. The proposed framework significantly reduces computational demands while maintaining high reconstruction quality, paving the way for scalable microstructure reconstruction in materials design and analysis. 

Abstract Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress–strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments. 

The rapid proliferation of the Internet of Things (IoT) necessitates compact, sustainable, and autonomous energy sources for distributed electronic devices. Microbial fuel cells (MFCs) offer an eco‐friendly alternative by converting organic matter into electrical energy using living micro‐organisms. However, their integration into microsystems faces significant challenges, including incompatibility with microfabrication, fragile anode materials, low electrical conductivity, and compromised microbial viability. Here, this study introduces a microscale biobattery platform integrating laser powder bed fusion‐fabricated 316L stainless steel anodes with resilient, spore‐formingBacillus subtilisbiocatalysts. The 3D‐printed gyroid scaffolds provide high surface‐to‐volume ratios, submillimeter porosity, and tunable roughness, enhancing microbial colonization and electron transfer. The stainless steel ensures mechanical robustness, chemical stability, and superior conductivity.Bacillus subtilisspores withstand harsh conditions, enabling prolonged storage and rapid, on‐demand activation. The biobattery produces 130 μW of power, exceeding conventional microscale MFCs, with exceptional reuse stability. A stack of six biobatteries achieves nearly 1 mW, successfully powering a 3.2‐inch thin‐film transistor liquid crystal display via capacitor‐assisted energy buffering, demonstrating practical applicability. This scalable, biologically resilient, and fabrication‐compatible solution advances autonomous electronic systems for IoT applications.