We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.

Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its built-in Bayesian regularisation and flexibility, essential qualities for physics related problems. Deriving the central learning objective for VI must often be tailored to new learning tasks where the nature of the problems dictates the conditional dependence between variables of interest, such as arising in physics problems. In this paper, we provide an accessible and thorough technical introduction to VI for forward and inverse problems, guiding the reader through standard derivations of the VI framework and how it can best be realized through deep learning. We then review and unify recent literature exemplifying the creative flexibility allowed by VI. This paper is designed for a general scientific audience looking to solve physics-based problems with an emphasis on uncertainty quantification.

Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly and time-consuming, especially when dealing with systems governed by complex physical laws which necessitates computationally intensive numerical methods such as finite element or finite volume techniques. On the other hand, surrogate-based methods offer an efficient alternative for computing reliability by approximating the underlying model from limited data. Neural operators have recently emerged as effective surrogates for modelling physical systems governed by partial differential equations. These operators can learn solutions to PDEs for varying inputs and parameters. Here, we investigate the efficacy of the recently developed physics-informed wavelet neural operator in solving reliability analysis problems. In particular, we investigate the possibility of using physics-informed operator for solving high-dimensional reliability analysis problems, while bypassing the need for any simulation. Through four numerical examples, we illustrate that physics-informed operator can seamlessly solve high-dimensional reliability analysis problems with reasonable accuracy, while eliminating the need for running expensive simulations.

Physics-informed machine learning (PIML) as a means of solving partial differential equations (PDE) has garnered much attention in the Computational Science and Engineering (CS&E) world. This topic encompasses a broad array of methods and models aimed at solving a single or a collection of PDE problems, called multitask learning. PIML is characterized by the incorporation of physical laws into the training process of machine learning models in lieu of large data when solving PDE problems. Despite the overall success of this collection of methods, it remains incredibly difficult to analyze, benchmark, and generally compare one approach to another. Using Kolmogorov n-widths as a measure of effectiveness of approximating functions, we judiciously apply this metric in the comparison of various multitask PIML architectures. We compute lower accuracy bounds and analyze the model's learned basis functions on various PDE problems. This is the first objective metric for comparing multitask PIML architectures and helps remove uncertainty in model validation from selective sampling and overfitting. We also identify avenues of improvement for model architectures, such as the choice of activation function, which can drastically affect model generalization to "worst-case" scenarios, which is not observed when reporting task-specific errors. We also incorporate this metric into the optimization process through regularization, which improves the models' generalizability over the multitask PDE problem.

Fine-tuning pre-trained models for downstream tasks has led to a proliferation of open-sourced task-specific models. Recently, Model Merging (MM) has emerged as an effective approach to facilitate knowledge transfer among these independently fine-tuned models. MM directly combines multiple fine-tuned task-specific models into a merged model without additional training, and the resulting model shows enhanced capabilities in multiple tasks. Although MM provides great utility, it may come with security risks because an adversary can exploit MM to affect multiple downstream tasks. However, the security risks of MM have barely been studied. In this paper, we first find that MM, as a new learning paradigm, introduces unique challenges for existing backdoor attacks due to the merging process. To address these challenges, we introduce BadMerging, the first backdoor attack specifically designed for MM. Notably, BadMerging allows an adversary to compromise the entire merged model by contributing as few as one backdoored task-specific model. BadMerging comprises a two-stage attack mechanism and a novel feature-interpolation-based loss to enhance the robustness of embedded backdoors against the changes of different merging parameters. Considering that a merged model may incorporate tasks from different domains, BadMerging can jointly compromise the tasks provided by the adversary (on-task attack) and other contributors (off-task attack) and solve the corresponding unique challenges with novel attack designs. Extensive experiments show that BadMerging achieves remarkable attacks against various MM algorithms. Our ablation study demonstrates that the proposed attack designs can progressively contribute to the attack performance. Finally, we show that prior defense mechanisms fail to defend against our attacks, highlighting the need for more advanced defense.

Context: Software Quality Assurance (SQA) is a fundamental part of software engineering to ensure stakeholders that software products work as expected after release in operation. Machine Learning (ML) has proven to be able to boost SQA activities and contribute to the development of quality software systems. In this context, Causal Reasoning is gaining increasing interest as a methodology to solve some of the current ML limitations. It aims to go beyond a purely data-driven approach by exploiting the use of causality for more effective SQA strategies. Objective: Provide a broad and detailed overview of the use of causal reasoning for SQA activities, in order to support researchers to access this research field, identifying room for application, main challenges and research opportunities. Methods: A systematic literature review of causal reasoning in the SQA research area. Scientific papers have been searched, classified, and analyzed according to established guidelines for software engineering secondary studies. Results: Results highlight the primary areas within SQA where causal reasoning has been applied, the predominant methodologies used, and the level of maturity of the proposed solutions. Fault localization is the activity where causal reasoning is more exploited, especially in the web services/microservices domain, but other tasks like testing are rapidly gaining popularity. Both causal inference and causal discovery are exploited, with the Pearl's graphical formulation of causality being preferred, likely due to its intuitiveness. Tools to favour their application are appearing at a fast pace - most of them after 2021. Conclusions: The findings show that causal reasoning is a valuable means for SQA tasks with respect to multiple quality attributes, especially during V&V, evolution and maintenance to ensure reliability, while it is not yet fully exploited for phases like ...

Large Language Models (LLMs) have showcased exceptional ability in causal reasoning from textual information. However, will these causalities remain straightforward for Vision Large Language Models (VLLMs) when only visual hints are provided? Motivated by this, we propose a novel Multimodal Causal Reasoning benchmark, namely MuCR, to challenge VLLMs to infer semantic cause-and-effect relationship when solely relying on visual cues such as action, appearance, clothing, and environment. Specifically, we introduce a prompt-driven image synthesis approach to create siamese images with embedded semantic causality and visual cues, which can effectively evaluate VLLMs' causal reasoning capabilities. Additionally, we develop tailored metrics from multiple perspectives, including image-level match, phrase-level understanding, and sentence-level explanation, to comprehensively assess VLLMs' comprehension abilities. Our extensive experiments reveal that the current state-of-the-art VLLMs are not as skilled at multimodal causal reasoning as we might have hoped. Furthermore, we perform a comprehensive analysis to understand these models' shortcomings from different views and suggest directions for future research. We hope MuCR can serve as a valuable resource and foundational benchmark in multimodal causal reasoning research. The project is available at: https://github.com/Zhiyuan-Li-John/MuCR

To address this gap, our study introduces the concept of causal epistemic consistency, which focuses on the self-consistency of Large Language Models (LLMs) in differentiating intermediates with nuanced differences in causal reasoning. We propose a suite of novel metrics -- intensity ranking concordance, cross-group position agreement, and intra-group clustering -- to evaluate LLMs on this front. Through extensive empirical studies on 21 high-profile LLMs, including GPT-4, Claude3, and LLaMA3-70B, we have favoring evidence that current models struggle to maintain epistemic consistency in identifying the polarity and intensity of intermediates in causal reasoning. Additionally, we explore the potential of using internal token probabilities as an auxiliary tool to maintain causal epistemic consistency. In summary, our study bridges a critical gap in AI research by investigating the self-consistency over fine-grained intermediates involved in causal reasoning.

Recent research in neural machine translation (NMT) has shown that training on high-quality machine-generated data can outperform training on human-generated data. This work accompanies the first-ever release of a LLM-generated, MBR-decoded and QE-reranked dataset with both sentence-level and multi-sentence examples. We perform extensive experiments to demonstrate the quality of our dataset in terms of its downstream impact on NMT model performance. We find that training from scratch on our (machine-generated) dataset outperforms training on the (web-crawled) WMT'23 training dataset (which is 300 times larger), and also outperforms training on the top-quality subset of the WMT'23 training dataset. We also find that performing self-distillation by finetuning the LLM which generated this dataset outperforms the LLM's strong few-shot baseline. These findings corroborate the quality of our dataset, and demonstrate the value of high-quality machine-generated data in improving performance of NMT models.

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.