The scientific computation of large deformations in elastic-plastic solids is crucial in various manufacturing applications. Traditional numerical methods exhibit several inherent limitations, prompting Deep Learning (DL) as a promising alternative. The effectiveness of current DL techniques typically depends on the availability of high-quantity and high-accuracy datasets, which are yet difficult to obtain in large deformation problems. During the dataset construction process, a dilemma stands between data quantity and data accuracy, leading to suboptimal performance in the DL models. To address this challenge, we focus on a representative application of large deformations, the stretch bending problem, and propose FilDeep, a Fidelity-based Deep Learning framework for large Deformation of elastic-plastic solids. Our FilDeep aims to resolve the quantity-accuracy dilemma by simultaneously training with both low-fidelity and high-fidelity data, where the former provides greater quantity but lower accuracy, while the latter offers higher accuracy but in less quantity. In FilDeep, we provide meticulous designs for the practical large deformation problem. Particularly, we propose attention-enabled cross-fidelity modules to effectively capture long-range physical interactions across MF data. To the best of our knowledge, our FilDeep presents the first DL framework for large deformation problems using MF data. Extensive experiments demonstrate that our FilDeep consistently achieves state-of-the-art performance and can be efficiently deployed in manufacturing.

In web-based systems, elements are commonly organized within a graph structure, with each node collecting essential spatio-temporal data. Examples include websites on the World Wide Web, traffic monitors in transportation networks, or sensors in the Internet of Things (IoT). However, sensors are typically deployed sparsely and unevenly, leaving the remaining nodes unobserved. The spatio-temporal kriging task, which infers values at unobserved nodes from observed ones, has thus attracted significant research interest. Due to limitations such as reliance on static graph structures and iterative Graph Convolution Network (GCN) frameworks, accurate kriging remains challenging. To address these issues, we propose a Diffusion-based Kriging Model with Graph-enhanced Attention (DKM-GA). Our approach first introduces a graph-enhanced attention mechanism that dynamically learns more accurate graph structures by combining predefined graph knowledge with global node value similarities. It is then integrated into a diffusion-based framework, which is tailored for the reliance of attention on known values. Therefore, the framework progressively refines the target values using correlated nodes, and the graph-enhanced attention selects more relevant neighbors based on the refined values. Furthermore, a node-based rescaling strategy is introduced to align the inference phase graphs to the training ones. Experiments on eight real-world datasets demonstrate that DKM-GA achieves superior performance, reducing estimation errors by up to 12.66%. Moreover, our analysis identifies three practical scenarios where the model delivers greater performance gains, even achieving 19.51% improvements on datasets that show minor gains under standard settings. These results highlight the effectiveness and potential of our model, while the scenarios provide settings for more comprehensive evaluations in terms of performance and robustness.

Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent trade-off between accuracy and efficiency. Recently, deep learning models have achieved impressive progress in solving the continuum mechanism. While previous models have explored various architectures and constructed coefficient-solution mappings, they are designed for general instances without considering specific problem properties and hard to accurately handle with complex elastic-plastic solids involving contact, loading and unloading. In this work, we take stretch bending, a popular metal fabrication technique, as our case study and introduce LaDEEP, a deep learning-based surrogate model for La rge De formation of Elastic-Plastic Solids. We encode the partitioned regions of the involved slender solids into a token sequence to maintain their essential order property. To characterize the physical process of the solid deformation, a two-stage Transformer-based module is designed to predict the deformation with the sequence of tokens as input. Empirically, LaDEEP achieves five magnitudes faster speed than finite element methods with a comparable accuracy, and gains 20.47% relative improvement on average compared to other deep learning baselines. We have also deployed our model into a real-world industrial production system, and it has shown remarkable performance in both accuracy and efficiency. Code is available at https://github.com/therontau0054/LaDEEP.

Regularization that incorporates the linear combination of empirical loss and explicit regularization terms as the loss function has been frequently used for many machine learning tasks. The explicit regularization term is designed in different types, depending on its applications. While regularized learning often boost the performance with higher accuracy and faster convergence, the regularization would sometimes hurt the empirical loss minimization and lead to poor performance. To deal with such issues in this work, we propose a novel strategy, namely Gr adients O rthogonal D ecomposition ( GrOD ), that improves the training procedure of regularized deep learning. Instead of linearly combining gradients of the two terms, GrOD re-estimates a new direction for iteration that does not hurt the empirical loss minimization while preserving the regularization affects, through orthogonal decomposition. We have performed extensive experiments to use GrOD improving the commonly used algorithms of transfer learning [ 2 ], knowledge distillation [ 3 ], and adversarial learning [ 4 ]. The experiment results based on large datasets, including Caltech 256 [ 5 ], MIT indoor 67 [ 6 ], CIFAR-10 [ 7 ], and ImageNet [ 8 ], show significant improvement made by GrOD for all three algorithms in all cases.

Stochastic Gradient Langevin Dynamics (SGLD) have been widely used for Bayesian sampling from certain probability distributions, incorporating derivatives of the log-posterior. With the derivative evaluation of the log-posterior distribution, SGLD methods generate samples from the distribution through performing as a thermostats dynamics that traverses over gradient flows of the log-posterior with certainly controllable perturbation. Even when the density is not known, existing solutions still can first learn the kernel density models from the given datasets, then produce new samples using the SGLD over the kernel density derivatives. In this work, instead of exploring new samples from kernel spaces, a novel SGLD sampler, namely, Randomized Measurement Langevin Dynamics (RMLD) is proposed to sample the high-dimensional sparse representations from the spectral domain of a given dataset. Specifically, given a random measurement matrix for sparse coding, RMLD first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the measurement matrix. The algorithm analysis shows that RMLD indeed projects a given dataset into a high-dimensional Gaussian distribution with Laplacian prior, then draw new sparse representation from the dataset through performing SGLD over the distribution. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of RMLD beyond baseline methods.

Transfer learning have been frequently used to improve deep neural network training through incorporating weights of pre-trained networks as the starting-point of optimization for regularization. While deep transfer learning can usually boost the performance with better accuracy and faster convergence, transferring weights from inappropriate networks hurts training procedure and may lead to even lower accuracy. In this paper, we consider deep transfer learning as minimizing a linear combination of empirical loss and regularizer based on pre-trained weights, where the regularizer would restrict the training procedure from lowering the empirical loss, with conflicted descent directions (e.g., derivatives). Following the view, we propose a novel strategy making regularization-based Deep Transfer learning Never Hurt (DTNH) that, for each iteration of training procedure, computes the derivatives of the two terms separately, then re-estimates a new descent direction that does not hurt the empirical loss minimization while preserving the regularization affects from the pre-trained weights. Extensive experiments have been done using common transfer learning regularizers, such as L2-SP and knowledge distillation, on top of a wide range of deep transfer learning benchmarks including Caltech, MIT indoor 67, CIFAR-10 and ImageNet. The empirical results show that the proposed descent direction estimation strategy DTNH can always improve the performance of deep transfer learning tasks based on all above regularizers, even when transferring pre-trained weights from inappropriate networks. All in all, DTNH strategy can improve state-of-the-art regularizers in all cases with 0.1%-7% higher accuracy in all experiments.