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Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affects the performance on a previous task trained by someone else. The authors developed a continual learning method that addresses this issue, applying it here for the first time to solid mechanics. In particular, the method is applied to recurrent neural networks to predict history-dependent plasticity behavior, although it can be used on any other architecture (feedforward, convolutional, etc.) and to predict other phenomena. This work intends to spawn future developments on continual learning that will foster cooperative strategies among the mechanics community to solve increasingly challenging problems. We show that the chosen continual learning strategy can sequentially learn several constitutive laws without forgetting them, using less data to achieve the same error as standard (non-cooperative) training of one law per model.

Deep neural networks are widely deployed in many fields. Due to the in-situ computation (known as processing in memory) capacity of the Resistive Random Access Memory (ReRAM) crossbar, ReRAM-based accelerator shows potential in accelerating DNN with low power and high performance. However, despite power advantage, such kind of accelerators suffer from the high power consumption of peripheral circuits, especially Analog-to-Digital Converter (ADC), which account for over 60 percent of total power consumption. This problem hinders the ReRAM-based accelerator to achieve higher efficiency. Some redundant Analog-to-Digital conversion operations have no contribution to maintaining inference accuracy, and such operations can be eliminated by modifying the ADC searching logic. Based on such observations, we propose an algorithm-hardware co-design method and explore the co-design approach in both hardware design and quantization algorithms. Firstly, we focus on the distribution output along the crossbar's bit-lines and identify the fine-grained redundant ADC sampling bits. % of weight and To further compress ADC bits, we propose a hardware-friendly quantization method and coding scheme, in which different quantization strategy was applied to the partial results in different intervals. To support the two features above, we propose a lightweight architectural design based on SAR-ADC\@. It's worth mentioning that our method is not only more energy efficient but also retains the flexibility of the algorithm. Experiments demonstrate that our method can reduce about $1.6 \sim 2.3 \times$ ADC power reduction.

The purpose of this study is to introduce a new approach to feature ranking for classification tasks, called in what follows greedy feature selection. In statistical learning, feature selection is usually realized by means of methods that are independent of the classifier applied to perform the prediction using that reduced number of features. Instead, greedy feature selection identifies the most important feature at each step and according to the selected classifier. In the paper, the benefits of such scheme are investigated theoretically in terms of model capacity indicators, such as the Vapnik-Chervonenkis (VC) dimension or the kernel alignment, and tested numerically by considering its application to the problem of predicting geo-effective manifestations of the active Sun.

Aqueous solubility is a valuable yet challenging property to predict. Computing solubility using first-principles methods requires accounting for the competing effects of entropy and enthalpy, resulting in long computations for relatively poor accuracy. Data-driven approaches, such as deep learning, offer improved accuracy and computational efficiency but typically lack uncertainty quantification. Additionally, ease of use remains a concern for any computational technique, resulting in the sustained popularity of group-based contribution methods. In this work, we addressed these problems with a deep learning model with predictive uncertainty that runs on a static website (without a server). This approach moves computing needs onto the website visitor without requiring installation, removing the need to pay for and maintain servers. Our model achieves satisfactory results in solubility prediction. Furthermore, we demonstrate how to create molecular property prediction models that balance uncertainty and ease of use. The code is available at //github.com/ur-whitelab/mol.dev, and the model is usable at //mol.dev.

One of the main challenges for interpreting black-box models is the ability to uniquely decompose square-integrable functions of non-independent random inputs into a sum of functions of every possible subset of variables. However, dealing with dependencies among inputs can be complicated. We propose a novel framework to study this problem, linking three domains of mathematics: probability theory, functional analysis, and combinatorics. We show that, under two reasonable assumptions on the inputs (non-perfect functional dependence and non-degenerate stochastic dependence), it is always possible to decompose such a function uniquely. This generalizes the well-known Hoeffding decomposition. The elements of this decomposition can be expressed using oblique projections and allow for novel interpretability indices for evaluation and variance decomposition purposes. The properties of these novel indices are studied and discussed. This generalization offers a path towards a more precise uncertainty quantification, which can benefit sensitivity analysis and interpretability studies whenever the inputs are dependent. This decomposition is illustrated analytically, and the challenges for adopting these results in practice are discussed.

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes equations yields a large sparse eigensystem, presenting challenges of slow convergence and high computational costs for implicit methods. To addresses this issue, the component-splitting method segregates the implicit operator into two parts: one for the flow equations (density/momentum/energy) and the other for the component equations. Each part's implicit operator employs flux-vector splitting based on their respective spectral radii to achieve accelerated convergence. This approach improves the computational efficiency of implicit iteration, mitigating the quadratic increase in time cost with the number of species. Two consistence corrections are developed to reduce the introduced component-splitting error and ensure the numerical consistency of mass fraction. Importantly, the impact of component-splitting method on accuracy is minimal as the residual approaches convergence. The accuracy, efficiency, and robustness of component-splitting method are thoroughly investigated and compared with the coupled implicit scheme through several numerical cases involving thermo-chemical nonequilibrium hypersonic flows. The results demonstrate that the component-splitting method decreases the required number of iteration steps for convergence of residual and wall heat flux, decreases the computation time per iteration step, and diminishes the residual to lower magnitude. The acceleration efficiency is enhanced with increases in CFL number and number of species.

During the evolution of large models, performance evaluation is necessarily performed to assess their capabilities and ensure safety before practical application. However, current model evaluations mainly rely on specific tasks and datasets, lacking a united framework for assessing the multidimensional intelligence of large models. In this perspective, we advocate for a comprehensive framework of cognitive science-inspired artificial general intelligence (AGI) tests, aimed at fulfilling the testing needs of large models with enhanced capabilities. The cognitive science-inspired AGI tests encompass the full spectrum of intelligence facets, including crystallized intelligence, fluid intelligence, social intelligence, and embodied intelligence. To assess the multidimensional intelligence of large models, the AGI tests consist of a battery of well-designed cognitive tests adopted from human intelligence tests, and then naturally encapsulates into an immersive virtual community. We propose increasing the complexity of AGI testing tasks commensurate with advancements in large models and emphasizing the necessity for the interpretation of test results to avoid false negatives and false positives. We believe that cognitive science-inspired AGI tests will effectively guide the targeted improvement of large models in specific dimensions of intelligence and accelerate the integration of large models into human society.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.