Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many applications, particularly in physical sciences and engineering, but also in areas such as geostatistics and neuroscience, invariance to symmetries is one of the most fundamental forms of prior information one can consider. The invariance of a Gaussian process' covariance to such symmetries gives rise to the most natural generalization of the concept of stationarity to such spaces. In this work, we develop constructive and practical techniques for building stationary Gaussian processes on a very large class of non-Euclidean spaces arising in the context of symmetries. Our techniques make it possible to (i) calculate covariance kernels and (ii) sample from prior and posterior Gaussian processes defined on such spaces, both in a practical manner. This work is split into two parts, each involving different technical considerations: part I studies compact spaces, while part II studies non-compact spaces possessing certain structure. Our contributions make the non-Euclidean Gaussian process models we study compatible with well-understood computational techniques available in standard Gaussian process software packages, thereby making them accessible to practitioners.

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore, the neural networks often struggle to converge when the solution to the real equation is very complex. Inspired by large eddy simulation in computational fluid dynamics, we propose an improved method based on filtering. We analyzed the causes of the difficulties in physics informed machine learning, and proposed a surrogate constraint (filtered PDE, FPDE in short) of the original physical equations to reduce the influence of noisy and sparse observation data. In the noise and sparsity experiment, the proposed FPDE models (which are optimized by FPDE constraints) have better robustness than the conventional PDE models. Experiments demonstrate that the FPDE model can obtain the same quality solution with 100% higher noise and 12% quantity of observation data of the baseline. Besides, two groups of real measurement data are used to show the FPDE improvements in real cases. The final results show that FPDE still gives more physically reasonable solutions when facing the incomplete equation problem and the extremely sparse and high-noise conditions. For combining real-world experiment data into physics-informed training, the proposed FPDE constraint is useful and performs well in two real-world experiments: modeling the blood velocity in vessels and cell migration in scratches.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. This method was explored on synthetic data from exoplanet transit light curve simulations. The true kernel was recovered in the low noise region while no kernel was preferred for larger noise. Furthermore, inference of the physical exoplanet hyperparameters was conducted. In the high noise region, either the bias in the posteriors was removed, the posteriors were broadened or the accuracy of the inference was increased. In addition, the uncertainty in mean function predictive distribution increased due to the uncertainty in the kernel choice. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, $H_0$, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and {\Lambda}CDM-dependent baryon acoustic oscillation observations. The inferred $H_0$ values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are $H_0$ = 66$\pm$6 km/s/Mpc, $H_0$ = 67$\pm$10 km/s/Mpc and $H_0$ = 69$\pm$6 km/s/Mpc, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln(R)=12.17$\pm$0.02.

Due to this uncertainty over which models will perform best, it is common place in the forecasting space that domain experts and data scientists have to experiment with several methods before they find one that works acceptably well on a particular problem. This exploration process can be time and resource consuming and is not always practical, due to the plethora of unsolved forecasting problems as well as the scarcity of domain experts and data scientists. In recent years, Automated Machine Learning (AutoML) has become more popular, allowing non-technical users to solve machine learning problems without in depth knowledge about the underlying methodology, filling in for the lack of available data scientists through automation [5]. In forecasting there are several approaches to AutoML, one of them being the established method of using ensemble learning and aggregation of forecasts [6]. This has seen a recent increase in attention, with the top performing models in the M4 Competition [7] being of this nature [8]. Ensembling, can be conceptualised as the automation of the previously manual step of exploring the performance of various algorithms on a given problem and selecting the best one or a combination of models. This, however, does not address another important aspect of data science which is the selection of good hyperparameters, leading to better performance of a model trained using a particular algorithm. The combination of ensemble learning and hyperparameter tuning in an AutoML forecasting setup will be discussed in this paper.

The advent of Industry 4.0 has precipitated the incorporation of Artificial Intelligence (AI) methods within industrial contexts, aiming to realize intelligent manufacturing, operation as well as maintenance, also known as industrial intelligence. However, intricate industrial milieus, particularly those relating to energy exploration and production, frequently encompass data characterized by long-tailed class distribution, sample imbalance, and domain shift. These attributes pose noteworthy challenges to data-centric Deep Learning (DL) techniques, crucial for the realization of industrial intelligence. The present study centers on the intricate and distinctive industrial scenarios of Nuclear Power Generation (NPG), meticulously scrutinizing the application of DL techniques under the constraints of finite data samples. Initially, the paper expounds on potential employment scenarios for AI across the full life-cycle of NPG. Subsequently, we delve into an evaluative exposition of DL's advancement, grounded in the finite sample perspective. This encompasses aspects such as small-sample learning, few-shot learning, zero-shot learning, and open-set recognition, also referring to the unique data characteristics of NPG. The paper then proceeds to present two specific case studies. The first revolves around the automatic recognition of zirconium alloy metallography, while the second pertains to open-set recognition for signal diagnosis of machinery sensors. These cases, spanning the entirety of NPG's life-cycle, are accompanied by constructive outcomes and insightful deliberations. By exploring and applying DL methodologies within the constraints of finite sample availability, this paper not only furnishes a robust technical foundation but also introduces a fresh perspective toward the secure and efficient advancement and exploitation of this advanced energy source.

Explainable Artificial Intelligence (XAI) is an emerging field in AI that aims to address the opaque nature of machine learning models. Furthermore, it has been shown that XAI can be used to extract input-output relationships, making them a useful tool in chemistry to understand structure-property relationships. However, one of the main limitations of XAI methods is that they are developed for technically oriented users. We propose the XpertAI framework that integrates XAI methods with large language models (LLMs) accessing scientific literature to generate accessible natural language explanations of raw chemical data automatically. We conducted 5 case studies to evaluate the performance of XpertAI. Our results show that XpertAI combines the strengths of LLMs and XAI tools in generating specific, scientific, and interpretable explanations.

This paper presents the real-world smart-meter dataset and offers an analysis of solutions derived from the Energy Prediction Technical Challenges, focusing primarily on two key competitions: the IEEE Computational Intelligence Society (IEEE-CIS) Technical Challenge on Energy Prediction from Smart Meter data in 2020 (named EP) and its follow-up challenge at the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) in 2021 (named as XEP). These competitions focus on accurate energy consumption forecasting and the importance of interpretability in understanding the underlying factors. The challenge aims to predict monthly and yearly estimated consumption for households, addressing the accurate billing problem with limited historical smart meter data. The dataset comprises 3,248 smart meters, with varying data availability ranging from a minimum of one month to a year. This paper delves into the challenges, solutions and analysing issues related to the provided real-world smart meter data, developing accurate predictions at the household level, and introducing evaluation criteria for assessing interpretability. Additionally, this paper discusses aspects beyond the competitions: opportunities for energy disaggregation and pattern detection applications at the household level, significance of communicating energy-driven factors for optimised billing, and emphasising the importance of responsible AI and data privacy considerations. These aspects provide insights into the broader implications and potential advancements in energy consumption prediction. Overall, these competitions provide a dataset for residential energy research and serve as a catalyst for exploring accurate forecasting, enhancing interpretability, and driving progress towards the discussion of various aspects such as energy disaggregation, demand response programs or behavioural interventions.

To reduce the heavy computational burden of reactive power optimization of distribution networks, machine learning models are receiving increasing attention. However, most machine learning models (e.g., neural networks) are usually considered as black boxes, making it challenging for power system operators to identify and comprehend potential biases or errors in the decision-making process of machine learning models. To address this issue, an explainable machine-learning framework is proposed to optimize the reactive power in distribution networks. Firstly, a Shapley additive explanation framework is presented to measure the contribution of each input feature to the solution of reactive power optimizations generated from machine learning models. Secondly, a model-agnostic approximation method is developed to estimate Shapley values, so as to avoid the heavy computational burden associated with direct calculations of Shapley values. The simulation results show that the proposed explainable framework can accurately explain the solution of the machine learning model-based reactive power optimization by using visual analytics, from both global and instance perspectives. Moreover, the proposed explainable framework is model-agnostic, and thus applicable to various models (e.g., neural networks).

Self-supervised learning has been actively studied in time series domain recently, especially for masked reconstruction. Most of these methods follow the "Pre-training + Fine-tuning" paradigm in which a new decoder replaces the pre-trained decoder to fit for a specific downstream task, leading to inconsistency of upstream and downstream tasks. In this paper, we first point out that the unification of task objectives and adaptation for task difficulty are critical for bridging the gap between time series masked reconstruction and forecasting. By reserving the pre-trained mask token during fine-tuning stage, the forecasting task can be taken as a special case of masked reconstruction, where the future values are masked and reconstructed based on history values. It guarantees the consistency of task objectives but there is still a gap in task difficulty. Because masked reconstruction can utilize contextual information while forecasting can only use historical information to reconstruct. To further mitigate the existed gap, we propose a simple yet effective prompt token tuning (PT-Tuning) paradigm, in which all pre-trained parameters are frozen and only a few trainable prompt tokens are added to extended mask tokens in element-wise manner. Extensive experiments on real-world datasets demonstrate the superiority of our proposed paradigm with state-of-the-art performance compared to representation learning and end-to-end supervised forecasting methods.

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to existing pretrained language models. We view diffusion and existing language models as complementary. We demonstrate that encoder-decoder language models can be utilized to efficiently learn high-quality language autoencoders. We then demonstrate that continuous diffusion models can be learned in the latent space of the language autoencoder, enabling us to sample continuous latent representations that can be decoded into natural language with the pretrained decoder. We validate the effectiveness of our approach for unconditional, class-conditional, and sequence-to-sequence language generation. We demonstrate across multiple diverse data sets that our latent language diffusion models are significantly more effective than previous diffusion language models.