Neural PDEs offer efficient alternatives to computationally expensive numerical PDE solvers for simulating complex physical systems. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we are able to quantify and calibrate the model's inconsistencies with the PDE rather than the uncertainty arising from the data. Our approach uses convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

While conditional diffusion models have achieved remarkable success in various applications, they require abundant data to train from scratch, which is often infeasible in practice. To address this issue, transfer learning has emerged as an essential paradigm in small data regimes. Despite its empirical success, the theoretical underpinnings of transfer learning conditional diffusion models remain unexplored. In this paper, we take the first step towards understanding the sample efficiency of transfer learning conditional diffusion models through the lens of representation learning. Inspired by practical training procedures, we assume that there exists a low-dimensional representation of conditions shared across all tasks. Our analysis shows that with a well-learned representation from source tasks, the samplecomplexity of target tasks can be reduced substantially. In addition, we investigate the practical implications of our theoretical results in several real-world applications of conditional diffusion models. Numerical experiments are also conducted to verify our results.

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian inference. We show that for a large class of transport maps $T$, there exists a time-dependent ODE velocity field realizing a straight-line interpolation $(1-t)x + tT(x)$, $t \in [0,1]$, of the displacement induced by the map. Moreover, we show that such velocity fields are minimizers of a training objective containing a specific minimum-energy regularization. We then derive explicit upper bounds for the $C^k$ norm of the velocity field that are polynomial in the $C^k$ norm of the corresponding transport map $T$; in the case of triangular (Knothe--Rosenblatt) maps, we also show that these bounds are polynomial in the $C^k$ norms of the associated source and target densities. Combining these results with stability arguments for distribution approximation via ODEs, we show that Wasserstein or Kullback--Leibler approximation of the target distribution to any desired accuracy $\epsilon > 0$ can be achieved by a deep neural network representation of the velocity field whose size is bounded explicitly in terms of $\epsilon$, the dimension, and the smoothness of the source and target densities. The same neural network ansatz yields guarantees on the value of the regularized training objective.

In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process. Traditional approaches, e.g., Markov-based and Gaussian process-based methods, typically leverage observations to estimate targets based on strong or fixed priors (such as Markov properties or Gaussian prior). However, the effectiveness of these methods depends on how well their prior assumptions align with the characteristics of the problem. When the assumed priors are not satisfied, these approaches may perform poorly or even become unusable. To overcome the above limitation, we introduce the Convolution-Based converter (CBC), which implicitly estimates the conditional probability distribution of targets without strong or fixed priors, and directly outputs the expected trajectory of the stochastic process that satisfies the constraints from observations. This approach reduces the dependence on priors, enhancing flexibility and adaptability in modeling stochastic processes when addressing different problems. Experimental results demonstrate that our method outperforms existing baselines across multiple metrics.

Student performance prediction is one of the most important subjects in educational data mining. As a modern technology, machine learning offers powerful capabilities in feature extraction and data modeling, providing essential support for diverse application scenarios, as evidenced by recent studies confirming its effectiveness in educational data mining. However, despite extensive prediction experiments, machine learning methods have not been effectively integrated into practical teaching strategies, hindering their application in modern education. In addition, massive features as input variables for machine learning algorithms often leads to information redundancy, which can negatively impact prediction accuracy. Therefore, how to effectively use machine learning methods to predict student performance and integrate the prediction results with actual teaching scenarios is a worthy research subject. To this end, this study integrates the results of machine learning-based student performance prediction with tiered instruction, aiming to enhance student outcomes in target course, which is significant for the application of educational data mining in contemporary teaching scenarios. Specifically, we collect original educational data and perform feature selection to reduce information redundancy. Then, the performance of five representative machine learning methods is analyzed and discussed with Random Forest showing the best performance. Furthermore, based on the results of the classification of students, tiered instruction is applied accordingly, and different teaching objectives and contents are set for all levels of students. The comparison of teaching outcomes between the control and experimental classes, along with the analysis of questionnaire results, demonstrates the effectiveness of the proposed framework.

Discriminative classifiers have become a foundational tool in deep learning for medical imaging, excelling at learning separable features of complex data distributions. However, these models often need careful design, augmentation, and training techniques to ensure safe and reliable deployment. Recently, diffusion models have become synonymous with generative modeling in 2D. These models showcase robustness across a range of tasks including natural image classification, where classification is performed by comparing reconstruction errors across images generated for each possible conditioning input. This work presents the first exploration of the potential of class conditional diffusion models for 2D medical image classification. First, we develop a novel majority voting scheme shown to improve the performance of medical diffusion classifiers. Next, extensive experiments on the CheXpert and ISIC Melanoma skin cancer datasets demonstrate that foundation and trained-from-scratch diffusion models achieve competitive performance against SOTA discriminative classifiers without the need for explicit supervision. In addition, we show that diffusion classifiers are intrinsically explainable, and can be used to quantify the uncertainty of their predictions, increasing their trustworthiness and reliability in safety-critical, clinical contexts. Further information is available on our project page: https://faverogian.github.io/med-diffusion-classifier.github.io/

Bayesian optimization (BO) has emerged as a powerful tool for guiding experimental design and decision- making in various scientific fields, including materials science, chemistry, and biology. However, despite its growing popularity, the complexity of existing BO libraries and the steep learning curve associated with them can deter researchers who are not well-versed in machine learning or programming. To address this barrier, we introduce Honegumi, a user-friendly, interactive tool designed to simplify the process of creating advanced Bayesian optimization scripts. Honegumi offers a dynamic selection grid that allows users to configure key parameters of their optimization tasks, generating ready-to-use, unit-tested Python scripts tailored to their specific needs. Accompanying the interface is a comprehensive suite of tutorials that provide both conceptual and practical guidance, bridging the gap between theoretical understanding and practical implementation. Built on top of the Ax platform, Honegumi leverages the power of existing state-of-the-art libraries while restructuring the user experience to make advanced BO techniques more accessible to experimental researchers. By lowering the barrier to entry and providing educational resources, Honegumi aims to accelerate the adoption of advanced Bayesian optimization methods across various domains.

Student simulation supports educators to improve teaching by interacting with virtual students. However, most existing approaches ignore the modulation effects of course materials because of two challenges: the lack of datasets with granularly annotated course materials, and the limitation of existing simulation models in processing extremely long textual data. To solve the challenges, we first run a 6-week education workshop from N = 60 students to collect fine-grained data using a custom built online education system, which logs students' learning behaviors as they interact with lecture materials over time. Second, we propose a transferable iterative reflection (TIR) module that augments both prompting-based and finetuning-based large language models (LLMs) for simulating learning behaviors. Our comprehensive experiments show that TIR enables the LLMs to perform more accurate student simulation than classical deep learning models, even with limited demonstration data. Our TIR approach better captures the granular dynamism of learning performance and inter-student correlations in classrooms, paving the way towards a ''digital twin'' for online education.

Artificial intelligence (AI) is increasingly being utilized to optimize magnetic resonance imaging (MRI) protocols. Given that image details are critical for diagnostic accuracy, optimizing MRI acquisition protocols is essential for enhancing image quality. While medical physicists are responsible for this optimization, the variability in equipment usage and the wide range of MRI protocols in clinical settings pose significant challenges. This study aims to validate the application of AI in optimizing MRI protocols using dynamic data from clinical practice, specifically DICOM metadata. To achieve this, four MRI spine exam databases were created, with the target attribute being the binary classification of image quality (good or bad). Five AI models were trained to identify trends in acquisition parameters that influence image quality, grounded in MRI theory. These trends were analyzed using SHAP graphs. The models achieved F1 performance ranging from 77% to 93% for datasets containing 292 or more instances, with the observed trends aligning with MRI theory. The models effectively reflected the practical realities of clinical MRI settings, offering a valuable tool for medical physicists in quality control tasks. In conclusion, AI has demonstrated its potential to optimize MRI protocols, supporting medical physicists in improving image quality and enhancing the efficiency of quality control in clinical practice.

This tutorial intends to introduce readers with a background in AI to quantum machine learning (QML) -- a rapidly evolving field that seeks to leverage the power of quantum computers to reshape the landscape of machine learning. For self-consistency, this tutorial covers foundational principles, representative QML algorithms, their potential applications, and critical aspects such as trainability, generalization, and computational complexity. In addition, practical code demonstrations are provided in https://qml-tutorial.github.io/ to illustrate real-world implementations and facilitate hands-on learning. Together, these elements offer readers a comprehensive overview of the latest advancements in QML. By bridging the gap between classical machine learning and quantum computing, this tutorial serves as a valuable resource for those looking to engage with QML and explore the forefront of AI in the quantum era.