Locking-Free Training of Physics-Informed Neural Network for Solving Nearly Incompressible Elasticity Equations

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible homogeneous elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio $\nu\to1/2$. This phenomenon, known as locking or non-robustness, remains not fully understood despite extensive investigation. In this paper, we propose a robust method based on a fundamentally different, machine-learning-driven approach. Leveraging recently developed Physics-Informed Neural Networks (PINNs), we address the numerical solution of linear elasticity equations governing nearly incompressible materials. The core idea of our method is to appropriately decompose the given equations to alleviate the extreme imbalance in the coefficients, while simultaneously solving both the forward and inverse problems to recover the solutions of the decomposed systems as well as the associated external conditions. Through various numerical experiments, including constant, variable and parametric Lam\'e coefficients, we illustrate the efficiency of the proposed methodology.

Engineering application of physics-informed neural networks for Saint-Venant torsion

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the finite element method (FEM), typically rely on mesh-based approaches to obtain approximate solutions. However, these methods often require complex and computationally intensive techniques to overcome the limitations of approximation, leading to significant increases in computational cost. The objective of this study is to develop a series of novel numerical methods based on physics-informed neural networks (PINN) for solving the Saint-Venant torsion equations. Utilizing the expressive power and the automatic differentiation capability of neural networks, the PINN can solve partial differential equations (PDEs) along with boundary conditions without the need for intricate computational techniques. First, a PINN solver was developed to compute the torsional constant for bars with arbitrary cross-sectional geometries. This was followed by the development of a solver capable of handling cases with sharp geometric transitions; variable-scaling PINN (VS-PINN). Finally, a parametric PINN was constructed to address the limitations of conventional single-instance PINN. The results from all three solvers showed good agreement with reference solutions, demonstrating their accuracy and robustness. Each solver can be selectively utilized depending on the specific requirements of torsional behavior analysis.

FRAIN to Train: A Fast-and-Reliable Solution for Decentralized Federated Learning

Federated learning (FL) enables collaborative model training across distributed clients while preserving data locality. Although FedAvg pioneered synchronous rounds for global model averaging, slower devices can delay collective progress. Asynchronous FL (e.g., FedAsync) addresses stragglers by continuously integrating client updates, yet naive implementations risk client drift due to non-IID data and stale contributions. Some Blockchain-based FL approaches (e.g., BRAIN) employ robust weighting or scoring of updates to resist malicious or misaligned proposals. However, performance drops can still persist under severe data heterogeneity or high staleness, and synchronization overhead has emerged as a new concern due to its aggregator-free architectures. We introduce Fast-and-Reliable AI Network, FRAIN, a new asynchronous FL method that mitigates these limitations by incorporating two key ideas. First, our FastSync strategy eliminates the need to replay past model versions, enabling newcomers and infrequent participants to efficiently approximate the global model. Second, we adopt spherical linear interpolation (SLERP) when merging parameters, preserving models' directions and alleviating destructive interference from divergent local training. Experiments with a CNN image-classification model and a Transformer-based language model demonstrate that FRAIN achieves more stable and robust convergence than FedAvg, FedAsync, and BRAIN, especially under harsh environments: non-IID data distributions, networks that experience delays and require frequent re-synchronization, and the presence of malicious nodes.

CURing Large Models: Compression via CUR Decomposition

Large deep learning models have achieved remarkable success but are resource-intensive, posing challenges in computational cost and memory usage. We introduce CURing, a novel model compression method based on CUR matrix decomposition, which approximates weight matrices as the product of selected columns (C) and rows (R), and a small linking matrix (U). We apply this decomposition to weights chosen based on the combined influence of their magnitudes and activations. By identifying and retaining informative rows and columns, CURing significantly reduces model size with minimal performance loss. It preserves the original network's input/output structures, retains important features such as non-negativity, and the compressed model's activation patterns align with the original, thereby enhancing interpretability.

A Blockchain-based Platform for Reliable Inference and Training of Large-Scale Models

As artificial intelligence (AI) continues to permeate various domains, concerns surrounding trust and transparency in AI-driven inference and training processes have emerged, particularly with respect to potential biases and traceability challenges. Decentralized solutions such as blockchain have been proposed to tackle these issues, but they often struggle when dealing with large-scale models, leading to time-consuming inference and inefficient training verification. To overcome these limitations, we introduce BRAIN, a Blockchain-based Reliable AI Network, a novel platform specifically designed to ensure reliable inference and training of large models. BRAIN harnesses a unique two-phase transaction mechanism, allowing real-time processing via pipelining by separating request and response transactions. Each randomly-selected inference committee commits and reveals the inference results, and upon reaching an agreement through a smart contract, then the requested operation is executed using the consensus result. Additionally, BRAIN carries out training by employing a randomly-selected training committee. They submit commit and reveal transactions along with their respective scores, enabling local model aggregation based on the median value of the scores. Experimental results demonstrate that BRAIN delivers considerably higher inference throughput at reasonable gas fees. In particular, BRAIN's tasks-per-second performance is 454.4293 times greater than that of a naive single-phase implementation.