A.1 Datasets We use two standardized few-shot image classification datasets. Mini-ImageNet: This dataset [58] is a subset of ImageNet [10] and consists of 64 classes for training, 16 for validation, and 20 for testing. There are 600 images per class, with images of size 84 84. Multiple versions of this dataset exist in the literature; we use the version by Ravi and Larochelle [43]. Tiered-ImageNet: A larger subset of ImageNet, Tiered-ImageNet [45] consists of 608 classes split into 351, 97, and 160 for training, validation, and testing, respectively.

Episodic training is a core ingredient of few-shot learning to train models on tasks with limited labelled data. Despite its success, episodic training remains largely understudied, prompting us to ask the question: what is the best way to sample episodes? In this paper, we first propose a method to approximate episode sampling distributions based on their difficulty. Building on this method, we perform an extensive analysis and find that sampling uniformly over episode difficulty outperforms other sampling schemes, including curriculum and easy-/hard-mining. As the proposed sampling method is algorithm agnostic, we can leverage these insights to improve few-shot learning accuracies across many episodic training algorithms. We demonstrate the efficacy of our method across popular few-shot learning datasets, algorithms, network architectures, and protocols.

In IMP, a multi-component engineering system is subject to a risk of failure due to its components' damage condition.

Multiple versions of this dataset exist in the literature; we use the version by Ravi and Larochelle [43]. The original version of the dataset contains43images that are also present in ImageNet. We remove these duplicates to avoid overestimating the transfer capability during evaluation. VGGFlowers: Originally introduced by Nilsback and Zisserman[38], VGGFlowers consists of 102 flower categories with each category containing between40 and 258 images. A.3 Trainingalgorithms For the metric-based family, we use ProtoNet with Euclidean [53] and scaled negative cosine similarity measures [20].

This paper introduces a sensor steering methodology based on deep reinforcement learning to enhance the predictive accuracy and decision support capabilities of digital twins by optimising the data acquisition process. Traditional sensor placement techniques are often constrained by one-off optimisation strategies, which limit their applicability for online applications requiring continuous informative data assimilation. The proposed approach addresses this limitation by offering an adaptive framework for sensor placement within the digital twin paradigm. The sensor placement problem is formulated as a Markov decision process, enabling the training and deployment of an agent capable of dynamically repositioning sensors in response to the evolving conditions of the physical structure as represented by the digital twin. This ensures that the digital twin maintains a highly representative and reliable connection to its physical counterpart. The proposed framework is validated through a series of comprehensive case studies involving a cantilever plate structure subjected to diverse conditions, including healthy and damaged conditions. The results demonstrate the capability of the deep reinforcement learning agent to adaptively reposition sensors improving the quality of data acquisition and hence enhancing the overall accuracy of digital twins.

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO surrogates to two popular surrogates used in fluid dynamics: the Dynamic Mode Decomposition and the Linearly-Recurrent Autoencoder Network. We regard Direct Numerical Simulations (DNS) of the RBC equations as the ground truth on which the models are trained and evaluated in different settings. The FNO performs favorably when compared to the DMD and LRAN and its predictions are fast and highly accurate for this task. Additionally, we show its zero-shot super-resolution ability for the convection dynamics. The FNO model has a high potential to be used in downstream tasks such as flow control in RBC.