Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when trying to approximate PDEs with dominant hyperbolic character. This research focuses on the development of a physics informed deep learning framework to approximate solutions to nonlinear PDEs that can develop shocks or discontinuities without any a-priori knowledge of the solution or the location of the discontinuities. The work takes motivation from finite element method that solves for solution values at nodes in the discretized domain and use these nodal values to obtain a globally defined solution field. Built on the rigorous mathematical foundations of the discontinuous Galerkin method, the framework naturally handles imposition of boundary conditions (Neumann/Dirichlet), entropy conditions, and regularity requirements. Several numerical experiments and validation with analytical solutions demonstrate the accuracy, robustness, and effectiveness of the proposed framework.
Recently, the remarkable capabilities of large language models (LLMs) have been illustrated across a variety of research domains such as natural language processing, computer vision, and molecular modeling. We extend this paradigm by utilizing LLMs for material property prediction by introducing our model Materials Informatics Transformer (MatInFormer). Specifically, we introduce a novel approach that involves learning the grammar of crystallography through the tokenization of pertinent space group information. We further illustrate the adaptability of MatInFormer by incorporating task-specific data pertaining to Metal-Organic Frameworks (MOFs). Through attention visualization, we uncover the key features that the model prioritizes during property prediction. The effectiveness of our proposed model is empirically validated across 14 distinct datasets, hereby underscoring its potential for high throughput screening through accurate material property prediction.
Ensembling a neural network is a widely recognized approach to enhance model performance, estimate uncertainty, and improve robustness in deep supervised learning. However, deep ensembles often come with high computational costs and memory demands. In addition, the efficiency of a deep ensemble is related to diversity among the ensemble members which is challenging for large, over-parameterized deep neural networks. Moreover, ensemble learning has not yet seen such widespread adoption, and it remains a challenging endeavor for self-supervised or unsupervised representation learning. Motivated by these challenges, we present a novel self-supervised training regime that leverages an ensemble of independent sub-networks, complemented by a new loss function designed to encourage diversity. Our method efficiently builds a sub-model ensemble with high diversity, leading to well-calibrated estimates of model uncertainty, all achieved with minimal computational overhead compared to traditional deep self-supervised ensembles. To evaluate the effectiveness of our approach, we conducted extensive experiments across various tasks, including in-distribution generalization, out-of-distribution detection, dataset corruption, and semi-supervised settings. The results demonstrate that our method significantly improves prediction reliability. Our approach not only achieves excellent accuracy but also enhances calibration, surpassing baseline performance across a wide range of self-supervised architectures in computer vision, natural language processing, and genomics data.
To handle graphs in which features or connectivities are evolving over time, a series of temporal graph neural networks (TGNNs) have been proposed. Despite the success of these TGNNs, the previous TGNN evaluations reveal several limitations regarding four critical issues: 1) inconsistent datasets, 2) inconsistent evaluation pipelines, 3) lacking workload diversity, and 4) lacking efficient comparison. Overall, there lacks an empirical study that puts TGNN models onto the same ground and compares them comprehensively. To this end, we propose BenchTemp, a general benchmark for evaluating TGNN models on various workloads. BenchTemp provides a set of benchmark datasets so that different TGNN models can be fairly compared. Further, BenchTemp engineers a standard pipeline that unifies the TGNN evaluation. With BenchTemp, we extensively compare the representative TGNN models on different tasks (e.g., link prediction and node classification) and settings (transductive and inductive), w.r.t. both effectiveness and efficiency metrics. We have made BenchTemp publicly available at //github.com/qianghuangwhu/benchtemp.
Statistical approaches that successfully combine multiple datasets are more powerful, efficient, and scientifically informative than separate analyses. To address variation architectures correctly and comprehensively for high-dimensional data across multiple sample sets (i.e., cohorts), we propose multiple augmented reduced rank regression (maRRR), a flexible matrix regression and factorization method to concurrently learn both covariate-driven and auxiliary structured variation. We consider a structured nuclear norm objective that is motivated by random matrix theory, in which the regression or factorization terms may be shared or specific to any number of cohorts. Our framework subsumes several existing methods, such as reduced rank regression and unsupervised multi-matrix factorization approaches, and includes a promising novel approach to regression and factorization of a single dataset (aRRR) as a special case. Simulations demonstrate substantial gains in power from combining multiple datasets, and from parsimoniously accounting for all structured variation. We apply maRRR to gene expression data from multiple cancer types (i.e., pan-cancer) from TCGA, with somatic mutations as covariates. The method performs well with respect to prediction and imputation of held-out data, and provides new insights into mutation-driven and auxiliary variation that is shared or specific to certain cancer types.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Graph Neural Networks (GNNs) are widely used for analyzing graph-structured data. Most GNN methods are highly sensitive to the quality of graph structures and usually require a perfect graph structure for learning informative embeddings. However, the pervasiveness of noise in graphs necessitates learning robust representations for real-world problems. To improve the robustness of GNN models, many studies have been proposed around the central concept of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding representations. Towards this end, in the presented survey, we broadly review recent progress of GSL methods for learning robust representations. Specifically, we first formulate a general paradigm of GSL, and then review state-of-the-art methods classified by how they model graph structures, followed by applications that incorporate the idea of GSL in other graph tasks. Finally, we point out some issues in current studies and discuss future directions.
Traffic forecasting is an important factor for the success of intelligent transportation systems. Deep learning models including convolution neural networks and recurrent neural networks have been applied in traffic forecasting problems to model the spatial and temporal dependencies. In recent years, to model the graph structures in the transportation systems as well as the contextual information, graph neural networks (GNNs) are introduced as new tools and have achieved the state-of-the-art performance in a series of traffic forecasting problems. In this survey, we review the rapidly growing body of recent research using different GNNs, e.g., graph convolutional and graph attention networks, in various traffic forecasting problems, e.g., road traffic flow and speed forecasting, passenger flow forecasting in urban rail transit systems, demand forecasting in ride-hailing platforms, etc. We also present a collection of open data and source resources for each problem, as well as future research directions. To the best of our knowledge, this paper is the first comprehensive survey that explores the application of graph neural networks for traffic forecasting problems. We have also created a public Github repository to update the latest papers, open data and source resources.
Graph neural networks (GNNs) have emerged as a powerful paradigm for embedding-based entity alignment due to their capability of identifying isomorphic subgraphs. However, in real knowledge graphs (KGs), the counterpart entities usually have non-isomorphic neighborhood structures, which easily causes GNNs to yield different representations for them. To tackle this problem, we propose a new KG alignment network, namely AliNet, aiming at mitigating the non-isomorphism of neighborhood structures in an end-to-end manner. As the direct neighbors of counterpart entities are usually dissimilar due to the schema heterogeneity, AliNet introduces distant neighbors to expand the overlap between their neighborhood structures. It employs an attention mechanism to highlight helpful distant neighbors and reduce noises. Then, it controls the aggregation of both direct and distant neighborhood information using a gating mechanism. We further propose a relation loss to refine entity representations. We perform thorough experiments with detailed ablation studies and analyses on five entity alignment datasets, demonstrating the effectiveness of AliNet.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.