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Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility in handling irregular and arbitrary input and output formats and scalability to large discretizations. Most existing architectures are limited by their desired structure or infeasible to scale large inputs and outputs. To address these issues, we introduce an attention-based model called an inducing-point operator transformer (IPOT). Inspired by inducing points methods, IPOT is designed to handle any input function and output query while capturing global interactions in a computationally efficient way. By detaching the inputs/outputs discretizations from the processor with a smaller latent bottleneck, IPOT offers flexibility in processing arbitrary discretizations and scales linearly with the size of inputs/outputs. Our experimental results demonstrate that IPOT achieves strong performances with manageable computational complexity on an extensive range of PDE benchmarks and real-world weather forecasting scenarios, compared to state-of-the-art methods.

Many current approaches to shrinkage within the time-varying parameter framework assume that each state is equipped with only one innovation variance for all time points. Sparsity is then induced by shrinking this variance towards zero. We argue that this is not sufficient if the states display large jumps or structural changes, something which is often the case in time series analysis. To remedy this, we propose the dynamic triple gamma prior, a stochastic process that has a well-known triple gamma marginal form, while still allowing for autocorrelation. Crucially, the triple gamma has many interesting limiting and special cases (including the horseshoe shrinkage prior) which can also be chosen as the marginal distribution. Not only is the marginal form well understood, we further derive many interesting properties of the dynamic triple gamma, which showcase its dynamic shrinkage characteristics. We develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior and demonstrate the performance through sparse covariance modeling and forecasting of the returns of the components of the EURO STOXX 50 index.

Low-order functional ANOVA (fANOVA) models have been rediscovered in the machine learning (ML) community under the guise of inherently interpretable machine learning. Explainable Boosting Machines or EBM (Lou et al. 2013) and GAMI-Net (Yang et al. 2021) are two recently proposed ML algorithms for fitting functional main effects and second-order interactions. We propose a new algorithm, called GAMI-Tree, that is similar to EBM, but has a number of features that lead to better performance. It uses model-based trees as base learners and incorporates a new interaction filtering method that is better at capturing the underlying interactions. In addition, our iterative training method converges to a model with better predictive performance, and the embedded purification ensures that interactions are hierarchically orthogonal to main effects. The algorithm does not need extensive tuning, and our implementation is fast and efficient. We use simulated and real datasets to compare the performance and interpretability of GAMI-Tree with EBM and GAMI-Net.

External and internal convertible (EIC) form-based motion control is one of the effective designs of simultaneously trajectory tracking and balance for underactuated balance robots. Under certain conditions, the EIC-based control design however leads to uncontrolled robot motion. We present a Gaussian process (GP)-based data-driven learning control for underactuated balance robots with the EIC modeling structure. Two GP-based learning controllers are presented by using the EIC structure property. The partial EIC (PEIC)-based control design partitions the robotic dynamics into a fully actuated subsystem and one reduced-order underactuated system. The null-space EIC (NEIC)-based control compensates for the uncontrolled motion in a subspace, while the other closed-loop dynamics are not affected. Under the PEIC- and NEIC-based, the tracking and balance tasks are guaranteed and convergence rate and bounded errors are achieved without causing any uncontrolled motion by the original EIC-based control. We validate the results and demonstrate the GP-based learning control design performance using two inverted pendulum platforms.

Using machine learning (ML) techniques to predict material properties is a crucial research topic. These properties depend on numerical data and semantic factors. Due to the limitations of small-sample datasets, existing methods typically adopt ML algorithms to regress numerical properties or transfer other pre-trained knowledge graphs (KGs) to the material. However, these methods cannot simultaneously handle semantic and numerical information. In this paper, we propose a numerical reasoning method for material KGs (NR-KG), which constructs a cross-modal KG using semantic nodes and numerical proxy nodes. It captures both types of information by projecting KG into a canonical KG and utilizes a graph neural network to predict material properties. In this process, a novel projection prediction loss is proposed to extract semantic features from numerical information. NR-KG facilitates end-to-end processing of cross-modal data, mining relationships and cross-modal information in small-sample datasets, and fully utilizes valuable experimental data to enhance material prediction. We further propose two new High-Entropy Alloys (HEA) property datasets with semantic descriptions. NR-KG outperforms state-of-the-art (SOTA) methods, achieving relative improvements of 25.9% and 16.1% on two material datasets. Besides, NR-KG surpasses SOTA methods on two public physical chemistry molecular datasets, showing improvements of 22.2% and 54.3%, highlighting its potential application and generalizability. We hope the proposed datasets, algorithms, and pre-trained models can facilitate the communities of KG and AI for materials.

Transformer architectures have facilitated the development of large-scale and general-purpose sequence models for prediction tasks in natural language processing and computer vision, e.g., GPT-3 and Swin Transformer. Although originally designed for prediction problems, it is natural to inquire about their suitability for sequential decision-making and reinforcement learning problems, which are typically beset by long-standing issues involving sample efficiency, credit assignment, and partial observability. In recent years, sequence models, especially the Transformer, have attracted increasing interest in the RL communities, spawning numerous approaches with notable effectiveness and generalizability. This survey presents a comprehensive overview of recent works aimed at solving sequential decision-making tasks with sequence models such as the Transformer, by discussing the connection between sequential decision-making and sequence modeling, and categorizing them based on the way they utilize the Transformer. Moreover, this paper puts forth various potential avenues for future research intending to improve the effectiveness of large sequence models for sequential decision-making, encompassing theoretical foundations, network architectures, algorithms, and efficient training systems. As this article has been accepted by the Frontiers of Computer Science, here is an early version, and the most up-to-date version can be found at //journal.hep.com.cn/fcs/EN/10.1007/s11704-023-2689-5

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.

Out-of-distribution (OOD) detection is critical to ensuring the reliability and safety of machine learning systems. For instance, in autonomous driving, we would like the driving system to issue an alert and hand over the control to humans when it detects unusual scenes or objects that it has never seen before and cannot make a safe decision. This problem first emerged in 2017 and since then has received increasing attention from the research community, leading to a plethora of methods developed, ranging from classification-based to density-based to distance-based ones. Meanwhile, several other problems are closely related to OOD detection in terms of motivation and methodology. These include anomaly detection (AD), novelty detection (ND), open set recognition (OSR), and outlier detection (OD). Despite having different definitions and problem settings, these problems often confuse readers and practitioners, and as a result, some existing studies misuse terms. In this survey, we first present a generic framework called generalized OOD detection, which encompasses the five aforementioned problems, i.e., AD, ND, OSR, OOD detection, and OD. Under our framework, these five problems can be seen as special cases or sub-tasks, and are easier to distinguish. Then, we conduct a thorough review of each of the five areas by summarizing their recent technical developments. We conclude this survey with open challenges and potential research directions.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.