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Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within PINNs to robustly accommodate geometric variations. Our method incorporates a diffeomorphism as a mapping of a reference domain and adapts the derivative computation of the physics-informed loss function. This generalizes the applicability of PINNs not only to smoothly deformed domains, but also to lower-dimensional manifolds and allows for direct shape optimization while training the network. We demonstrate the effectivity of our approach on several problems: (i) Eikonal equation on Archimedean spiral, (ii) Poisson problem on surface manifold, (iii) Incompressible Stokes flow in deformed tube, and (iv) Shape optimization with Laplace operator. Through these examples, we demonstrate the enhanced flexibility over traditional PINNs, especially under geometric variations. The proposed framework presents an outlook for training deep neural operators over parametrized geometries, paving the way for advanced modeling with PDEs on complex geometries in science and engineering.

In this paper, a new method based on TOPSIS and optimization models is proposed for multi-attribute group decision-making in the environment of interval-valued intuitionistic fuzzy sets.Firstly, by minimizing the sum of differences between individual evaluations and the overallconsistent evaluations of all experts, a new optimization model is established for determining expert weights. Secondly, based on TOPSIS method, the improved closeness index for evaluating each alternative is obtained. Finally, the attribute weight is determined by establishing an optimization model with the goal of maximizing the closeness of each alternative, and it is brought into the closeness index so that the alternatives can be ranked. Combining all these together, the complete fuzzy multi-attribute group decision-making algorithm is formulated, which can give full play to the advantages of subjective and objective weighting methods. In the end, the feasibility and effectiveness of the provided method are verified by a real case study.

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.

Advancements in artificial intelligence (AI) over the last decade demonstrate that machines can exhibit communicative behavior and influence how humans think, feel, and behave. In fact, the recent development of ChatGPT has shown that large language models (LLMs) can be leveraged to generate high-quality communication content at scale and across domains, suggesting that they will be increasingly used in practice. However, many questions remain about how knowing the source of the messages influences recipients' evaluation of and preference for AI-generated messages compared to human-generated messages. This paper investigated this topic in the context of vaping prevention messaging. In Study 1, which was pre-registered, we examined the influence of source disclosure on people's evaluation of AI-generated health prevention messages compared to human-generated messages. We found that source disclosure (i.e., labeling the source of a message as AI vs. human) significantly impacted the evaluation of the messages but did not significantly alter message rankings. In a follow-up study (Study 2), we examined how the influence of source disclosure may vary by the participants' negative attitudes towards AI. We found a significant moderating effect of negative attitudes towards AI on message evaluation, but not for message selection. However, for those with moderate levels of negative attitudes towards AI, source disclosure decreased the preference for AI-generated messages. Overall, the results of this series of studies showed a slight bias against AI-generated messages once the source was disclosed, adding to the emerging area of study that lies at the intersection of AI and communication.

A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution generating the data. We observe that the maximum likelihood problem for the Cauchy distributions, which have particularly heavy tails, is geodesically convex and therefore efficiently solvable (Cauchy distributions are parametrized by the upper half plane, i.e. by the hyperbolic plane). Moreover, it has an appealing geometrical meaning: the datapoints, living on the boundary of the hyperbolic plane, are attracting the parameter by unit forces, and we search the point where these forces are in equilibrium. This picture generalizes to several classes of multivariate distributions with heavy tails, including, in particular, the multivariate Cauchy distributions. The hyperbolic plane gets replaced by symmetric spaces of noncompact type. Geodesic convexity gives us an efficient numerical solution of the maximum likelihood problem for these distribution classes. This can then be used for robust estimates of location and spread, thanks to the heavy tails of these distributions.

In this paper, we propose a computational interpretation of the generalized Kreisel-Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry-Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for the intuitionistic propositional logic. This will guide our process of formulating an appropriate program that would capture the corresponding computational content of the typed Split rule. In other words, we want to find an appropriate selector function for the Split rule by considering its typed variant. Our investigation can also be reframed as an effort to answer the following questions: is the Split rule constructively valid in the sense of BHK semantics? Our answer is positive for the Split rule as well as for its newly proposed generalized version called the S rule.

Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation of gradients for machine learning or other differentiable programming tasks. We develop novel algorithmic structures for accelerated and differentiable computation of generalised Fourier transforms on the sphere $\mathbb{S}^2$ and rotation group $\text{SO}(3)$, i.e. spherical harmonic and Wigner transforms, respectively. We present a recursive algorithm for the calculation of Wigner $d$-functions that is both stable to high harmonic degrees and extremely parallelisable. By tightly coupling this with separable spherical transforms, we obtain algorithms that exhibit an extremely parallelisable structure that is well-suited for the high throughput computing of modern hardware accelerators (e.g. GPUs). We also develop a hybrid automatic and manual differentiation approach so that gradients can be computed efficiently. Our algorithms are implemented within the JAX differentiable programming framework in the S2FFT software code. Numerous samplings of the sphere are supported, including equiangular and HEALPix sampling. Computational errors are at the order of machine precision for spherical samplings that admit a sampling theorem. When benchmarked against alternative C codes we observe up to a 400-fold acceleration. Furthermore, when distributing over multiple GPUs we achieve very close to optimal linear scaling with increasing number of GPUs due to the highly parallelised and balanced nature of our algorithms. Provided access to sufficiently many GPUs our transforms thus exhibit an unprecedented effective linear time complexity.

Previous researchers conducting Just-In-Time (JIT) defect prediction tasks have primarily focused on the performance of individual pre-trained models, without exploring the relationship between different pre-trained models as backbones. In this study, we build six models: RoBERTaJIT, CodeBERTJIT, BARTJIT, PLBARTJIT, GPT2JIT, and CodeGPTJIT, each with a distinct pre-trained model as its backbone. We systematically explore the differences and connections between these models. Specifically, we investigate the performance of the models when using Commit code and Commit message as inputs, as well as the relationship between training efficiency and model distribution among these six models. Additionally, we conduct an ablation experiment to explore the sensitivity of each model to inputs. Furthermore, we investigate how the models perform in zero-shot and few-shot scenarios. Our findings indicate that each model based on different backbones shows improvements, and when the backbone's pre-training model is similar, the training resources that need to be consumed are much more closer. We also observe that Commit code plays a significant role in defect detection, and different pre-trained models demonstrate better defect detection ability with a balanced dataset under few-shot scenarios. These results provide new insights for optimizing JIT defect prediction tasks using pre-trained models and highlight the factors that require more attention when constructing such models. Additionally, CodeGPTJIT and GPT2JIT achieved better performance than DeepJIT and CC2Vec on the two datasets respectively under 2000 training samples. These findings emphasize the effectiveness of transformer-based pre-trained models in JIT defect prediction tasks, especially in scenarios with limited training data.

In this paper, we introduce an Abaqus UMAT subroutine for a family of constitutive models for the viscoelastic response of isotropic elastomers of any compressibility -- including fully incompressible elastomers -- undergoing finite deformations. The models can be chosen to account for a wide range of non-Gaussian elasticities, as well as for a wide range of nonlinear viscosities. From a mathematical point of view, the structure of the models is such that the viscous dissipation is characterized by an internal variable $\textbf{C}^v$, subject to the physically-based constraint $\det\textbf{C}^v=1$, that is solution of a nonlinear first-order ODE in time. This ODE is solved by means of an explicit Runge-Kutta scheme of high order capable of preserving the constraint $\det\textbf{C}^v=1$ identically. The accuracy and convergence of the code is demonstrated numerically by comparison with an exact solution for several of the Abaqus built-in hybrid finite elements, including the simplicial elements C3D4H and C3D10H and the hexahedral elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing the capabilities of the code by deploying it to compute the homogenized response of a bicontinuous rubber blend.

End-to-end relation extraction (E2ERE) is an important and realistic application of natural language processing (NLP) in biomedicine. In this paper, we aim to compare three prevailing paradigms for E2ERE using a complex dataset focused on rare diseases involving discontinuous and nested entities. We use the RareDis information extraction dataset to evaluate three competing approaches (for E2ERE): NER $\rightarrow$ RE pipelines, joint sequence to sequence models, and generative pre-trained transformer (GPT) models. We use comparable state-of-the-art models and best practices for each of these approaches and conduct error analyses to assess their failure modes. Our findings reveal that pipeline models are still the best, while sequence-to-sequence models are not far behind; GPT models with eight times as many parameters are worse than even sequence-to-sequence models and lose to pipeline models by over 10 F1 points. Partial matches and discontinuous entities caused many NER errors contributing to lower overall E2E performances. We also verify these findings on a second E2ERE dataset for chemical-protein interactions. Although generative LM-based methods are more suitable for zero-shot settings, when training data is available, our results show that it is better to work with more conventional models trained and tailored for E2ERE. More innovative methods are needed to marry the best of the both worlds from smaller encoder-decoder pipeline models and the larger GPT models to improve E2ERE. As of now, we see that well designed pipeline models offer substantial performance gains at a lower cost and carbon footprint for E2ERE. Our contribution is also the first to conduct E2ERE for the RareDis dataset.