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This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the improvement of additive manufacturing as they offer, among many others, excellent stiffness-to-weight ratios. We develop here a dedicated HPC solver that benefits from the specific nature of the underlying problem in order to drastically reduce the computational costs (memory and time) for the full fine-scale analysis of lattice structures. Our purpose is to take advantage of the natural domain decomposition into cells and, even more importantly, of the geometrical and mechanical similarities among cells. Our solver consists in a so-called inexact FETI-DP method where the local, cell-wise operators and solutions are approximated with reduced order modeling techniques. Instead of considering independently every cell, we end up with only few principal local problems to solve and make use of the corresponding principal cell-wise operators to approximate all the others. It results in a scalable algorithm that saves numerous local factorizations. Our solver is applied for the isogeometric analysis of lattices built by spline composition, which offers the opportunity to compute the reduced basis with macro-scale data, thereby making our method also multiscale and matrix-free. The solver is tested against various 2D and 3D analyses. It shows major gains with respect to black-box solvers; in particular, problems of several millions of degrees of freedom can be solved with a simple computer within few minutes.

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson classification (NPC) and fairness classification, which entail specific risk constraints that render standard projection-based training algorithms unsuitable. Gradient boosting machines (GBMs) are among the most popular algorithms for supervised learning; however, they are generally limited to unconstrained settings. In this paper, we adapt the GBM for constrained learning tasks within the framework of Bregman proximal algorithms. We introduce a new Bregman primal-dual method with a global optimality guarantee when the learning objective and constraint functions are convex. In cases of nonconvex functions, we demonstrate how our algorithm remains effective under a Bregman proximal point framework. Distinct from existing constrained learning algorithms, ours possess a unique advantage in their ability to seamlessly integrate with publicly available GBM implementations such as XGBoost (Chen and Guestrin, 2016) and LightGBM (Ke et al., 2017), exclusively relying on their public interfaces. We provide substantial experimental evidence to showcase the effectiveness of the Bregman algorithm framework. While our primary focus is on NPC and fairness ML, our framework holds significant potential for a broader range of constrained learning applications. The source code is currently freely available at //github.com/zhenweilin/ConstrainedGBM}{//github.com/zhenweilin/ConstrainedGBM.

Out-of-distribution detection is one of the most critical issue in the deployment of machine learning. The data analyst must assure that data in operation should be compliant with the training phase as well as understand if the environment has changed in a way that autonomous decisions would not be safe anymore. The method of the paper is based on eXplainable Artificial Intelligence (XAI); it takes into account different metrics to identify any resemblance between in-distribution and out of, as seen by the XAI model. The approach is non-parametric and distributional assumption free. The validation over complex scenarios (predictive maintenance, vehicle platooning, covert channels in cybersecurity) corroborates both precision in detection and evaluation of training-operation conditions proximity. Results are available via open source and open data at the following link: //github.com/giacomo97cnr/Rule-based-ODD.

Counterfactual explanations are an emerging tool to enhance interpretability of deep learning models. Given a sample, these methods seek to find and display to the user similar samples across the decision boundary. In this paper, we propose a generative adversarial counterfactual approach for satellite image time series in a multi-class setting for the land cover classification task. One of the distinctive features of the proposed approach is the lack of prior assumption on the targeted class for a given counterfactual explanation. This inherent flexibility allows for the discovery of interesting information on the relationship between land cover classes. The other feature consists of encouraging the counterfactual to differ from the original sample only in a small and compact temporal segment. These time-contiguous perturbations allow for a much sparser and, thus, interpretable solution. Furthermore, plausibility/realism of the generated counterfactual explanations is enforced via the proposed adversarial learning strategy.

Graph representation learning (GRL) methods, such as graph neural networks and graph transformer models, have been successfully used to analyze graph-structured data, mainly focusing on node classification and link prediction tasks. However, the existing studies mostly only consider local connectivity while ignoring long-range connectivity and the roles of nodes. In this paper, we propose Unified Graph Transformer Networks (UGT) that effectively integrate local and global structural information into fixed-length vector representations. First, UGT learns local structure by identifying the local substructures and aggregating features of the $k$-hop neighborhoods of each node. Second, we construct virtual edges, bridging distant nodes with structural similarity to capture the long-range dependencies. Third, UGT learns unified representations through self-attention, encoding structural distance and $p$-step transition probability between node pairs. Furthermore, we propose a self-supervised learning task that effectively learns transition probability to fuse local and global structural features, which could then be transferred to other downstream tasks. Experimental results on real-world benchmark datasets over various downstream tasks showed that UGT significantly outperformed baselines that consist of state-of-the-art models. In addition, UGT reaches the expressive power of the third-order Weisfeiler-Lehman isomorphism test (3d-WL) in distinguishing non-isomorphic graph pairs. The source code is available at //github.com/NSLab-CUK/Unified-Graph-Transformer.

Multi-objective Markov decision processes are a special kind of multi-objective optimization problem that involves sequential decision making while satisfying the Markov property of stochastic processes. Multi-objective reinforcement learning methods address this problem by fusing the reinforcement learning paradigm with multi-objective optimization techniques. One major drawback of these methods is the lack of adaptability to non-stationary dynamics in the environment. This is because they adopt optimization procedures that assume stationarity to evolve a coverage set of policies that can solve the problem. This paper introduces a developmental optimization approach that can evolve the policy coverage set while exploring the preference space over the defined objectives in an online manner. We propose a novel multi-objective reinforcement learning algorithm that can robustly evolve a convex coverage set of policies in an online manner in non-stationary environments. We compare the proposed algorithm with two state-of-the-art multi-objective reinforcement learning algorithms in stationary and non-stationary environments. Results showed that the proposed algorithm significantly outperforms the existing algorithms in non-stationary environments while achieving comparable results in stationary environments.

A new generalization of Reed-Solomon codes is given. This new generalization has similar information rate bound and similar distance rate bound as BCH codes. It also approaches to the Gilbert bound as Goppa codes. Nevertheless, decoding these new codes is much faster than decoding BCH codes.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.