In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise polynomials to approximate various characteristics of a problem, such as the concentration profile and the temperature distribution across the domain. Polynomials are prone to creating artifacts such as Gibbs oscillations while capturing a complex profile. An efficient and accurate approach must be applied to deal with such inconsistencies in order to obtain accurate simulations. This often entails dealing with negative values for the concentration of chemicals, exceeding a percentage value over 100, and other such problems. We consider these inconsistencies in the context of partial differential equations (PDEs). We propose an innovative filter based on convex optimization to deal with the inconsistencies observed in polynomial-based simulations. In two or three spatial dimensions, additional complexities are involved in solving the problems related to structure preservation. We present the construction and application of a structure-preserving filter with a focus on multidimensional PDEs. Methods used such as the Barycentric interpolation for polynomial evaluation at arbitrary points in the domain and an optimized root-finder to identify points of interest improve the filter efficiency, usability, and robustness. Lastly, we present numerical experiments in 2D and 3D using discontinuous Galerkin formulation and demonstrate the filter's efficacy to preserve the desired structure. As a real-world application, implementation of the mathematical biology model involving platelet aggregation and blood coagulation has been reviewed and the issues around FEM implementation of the model are resolved by applying the proposed structure-preserving filter.
相關內容
Model Checking is widely applied in verifying complicated and especially concurrent systems. Despite of its popularity, model checking suffers from the state space explosion problem that restricts it from being applied to certain systems, or specifications. Many works have been proposed in the past to address the state space explosion problem, and they have achieved some success, but the inherent complexity still remains an obstacle for purely symbolic approaches. In this paper, we propose a Graph Neural Network (GNN) based approach for model checking, where the model is expressed using a B{\"u}chi automaton and the property to be verified is expressed using Linear Temporal Logic (LTL). We express the model as a GNN, and propose a novel node embedding framework that encodes the LTL property and characteristics of the model. We reduce the LTL model checking problem to a graph classification problem, where there are two classes, 1 (if the model satisfies the specification) and 0 (if the model does not satisfy the specification). The experimental results show that our framework is up to 17 times faster than state-of-the-art tools. Our approach is particularly useful when dealing with very large LTL formulae and small to moderate sized models.
Hyperparameter optimization (HPO) is important to leverage the full potential of machine learning (ML). In practice, users are often interested in multi-objective (MO) problems, i.e., optimizing potentially conflicting objectives, like accuracy and energy consumption. To tackle this, the vast majority of MO-ML algorithms return a Pareto front of non-dominated machine learning models to the user. Optimizing the hyperparameters of such algorithms is non-trivial as evaluating a hyperparameter configuration entails evaluating the quality of the resulting Pareto front. In literature, there are known indicators that assess the quality of a Pareto front (e.g., hypervolume, R2) by quantifying different properties (e.g., volume, proximity to a reference point). However, choosing the indicator that leads to the desired Pareto front might be a hard task for a user. In this paper, we propose a human-centered interactive HPO approach tailored towards multi-objective ML leveraging preference learning to extract desiderata from users that guide the optimization. Instead of relying on the user guessing the most suitable indicator for their needs, our approach automatically learns an appropriate indicator. Concretely, we leverage pairwise comparisons of distinct Pareto fronts to learn such an appropriate quality indicator. Then, we optimize the hyperparameters of the underlying MO-ML algorithm towards this learned indicator using a state-of-the-art HPO approach. In an experimental study targeting the environmental impact of ML, we demonstrate that our approach leads to substantially better Pareto fronts compared to optimizing based on a wrong indicator pre-selected by the user, and performs comparable in the case of an advanced user knowing which indicator to pick.
Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based setting can lead to an adversarial framework where the discriminator provides unnormalized density (often called energy). We further develop this perspective, incorporate importance sampling, and show that 1) Wasserstein GAN performs a biased estimate of the partition function, and we propose instead to use an unbiased estimator; and 2) when optimizing for likelihood, one must maximize generator entropy. This is hypothesized to provide a better mode coverage. Different from previous works, we explicitly compute the density of the generated samples. This is the key enabler to designing an unbiased estimator of the partition function and computation of the generator entropy term. The generator density is obtained via a new type of flow network, called one-way flow network, that is less constrained in terms of architecture, as it does not require a tractable inverse function. Our experimental results show that our method converges faster, produces comparable sample quality to GANs with similar architecture, successfully avoids over-fitting to commonly used datasets and produces smooth low-dimensional latent representations of the training data.
While recommender systems have significantly benefited from implicit feedback, they have often missed the nuances of multi-behavior interactions between users and items. Historically, these systems either amalgamated all behaviors, such as \textit{impression} (formerly \textit{view}), \textit{add-to-cart}, and \textit{buy}, under a singular 'interaction' label, or prioritized only the target behavior, often the \textit{buy} action, discarding valuable auxiliary signals. Although recent advancements tried addressing this simplification, they primarily gravitated towards optimizing the target behavior alone, battling with data scarcity. Additionally, they tended to bypass the nuanced hierarchy intrinsic to behaviors. To bridge these gaps, we introduce the \textbf{H}ierarchical \textbf{M}ulti-behavior \textbf{G}raph Attention \textbf{N}etwork (HMGN). This pioneering framework leverages attention mechanisms to discern information from both inter and intra-behaviors while employing a multi-task Hierarchical Bayesian Personalized Ranking (HBPR) for optimization. Recognizing the need for scalability, our approach integrates a specialized multi-behavior sub-graph sampling technique. Moreover, the adaptability of HMGN allows for the seamless inclusion of knowledge metadata and time-series data. Empirical results attest to our model's prowess, registering a notable performance boost of up to 64\% in NDCG@100 metrics over conventional graph neural network methods.
Ising machines have emerged as a promising solution for rapidly solving NP-complete combinatorial optimization problems, surpassing the capabilities of traditional computing methods. By efficiently determining the ground state of the Hamiltonian during the annealing process, Ising machines can effectively complement CPUs in tackling optimization challenges. To realize these Ising machines, a bi-stable oscillator is essential to emulate the atomic spins and interactions of the Ising model. This study introduces a Josephson parametric oscillator (JPO)-based tile structure, serving as a fundamental unit for scalable superconductor-based Ising machines. Leveraging the bi-stable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of 7.5GHz while consuming significantly less power (by three orders of magnitude) than CMOS-based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller (LHZ) architecture ensures its viability for large-scale integration. We conducted simulations of the tile in a noisy environment to validate its functionality. We verified its operational characteristics by comparing the results with the analytical solution of its Hamiltonian model. This verification demonstrates the feasibility and effectiveness of the JPO-based tile in implementing Ising machines, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.
The Ultra Weak Variational Formulation (UWVF) is a special Trefftz discontinuous Galerkin method, here applied to the time-harmonic Maxwell's equations. The method uses superpositions of plane waves to represent solutions element by element on a finite element mesh. We discuss the use of our parallel UWVF implementation called ParMax, and concentrate on methods for obtaining high order solutions in the presence of scatterers with piecewise smooth boundaries. In particular, we show how curved surface triangles can be incorporated in the UWVF. This requires quadrature to assemble the system matrices. We also show how to implement a total field and scattered field approach, together with the transmission conditions across an interface to handle resistive sheets. We note also that a wide variety of element shapes can be used, that the elements can be large compared to the wavelength of the radiation, and that a matrix free version is easy to implement (although computationally costly). Our contributions are illustrated by several numerical examples showing that curved elements can improve the efficiency of the UWVF, and that the method accurately handles resistive screens as well as PEC and penetrable scatterers. Using large curved elements and the matrix free approach, we are able to simulate scattering from an aircraft at X-band frequencies. The innovations here demonstrate the applicability of the UWVF for industrial examples.
This paper focuses on the problem of semi-supervised domain adaptation for time-series forecasting, which is underexplored in literatures, despite being often encountered in practice. Existing methods on time-series domain adaptation mainly follow the paradigm designed for the static data, which cannot handle domain-specific complex conditional dependencies raised by data offset, time lags, and variant data distributions. In order to address these challenges, we analyze variational conditional dependencies in time-series data and find that the causal structures are usually stable among domains, and further raise the causal conditional shift assumption. Enlightened by this assumption, we consider the causal generation process for time-series data and propose an end-to-end model for the semi-supervised domain adaptation problem on time-series forecasting. Our method can not only discover the Granger-Causal structures among cross-domain data but also address the cross-domain time-series forecasting problem with accurate and interpretable predicted results. We further theoretically analyze the superiority of the proposed method, where the generalization error on the target domain is bounded by the empirical risks and by the discrepancy between the causal structures from different domains. Experimental results on both synthetic and real data demonstrate the effectiveness of our method for the semi-supervised domain adaptation method on time-series forecasting.
Recent artificial intelligence (AI) systems have reached milestones in "grand challenges" ranging from Go to protein-folding. The capability to retrieve medical knowledge, reason over it, and answer medical questions comparably to physicians has long been viewed as one such grand challenge. Large language models (LLMs) have catalyzed significant progress in medical question answering; Med-PaLM was the first model to exceed a "passing" score in US Medical Licensing Examination (USMLE) style questions with a score of 67.2% on the MedQA dataset. However, this and other prior work suggested significant room for improvement, especially when models' answers were compared to clinicians' answers. Here we present Med-PaLM 2, which bridges these gaps by leveraging a combination of base LLM improvements (PaLM 2), medical domain finetuning, and prompting strategies including a novel ensemble refinement approach. Med-PaLM 2 scored up to 86.5% on the MedQA dataset, improving upon Med-PaLM by over 19% and setting a new state-of-the-art. We also observed performance approaching or exceeding state-of-the-art across MedMCQA, PubMedQA, and MMLU clinical topics datasets. We performed detailed human evaluations on long-form questions along multiple axes relevant to clinical applications. In pairwise comparative ranking of 1066 consumer medical questions, physicians preferred Med-PaLM 2 answers to those produced by physicians on eight of nine axes pertaining to clinical utility (p < 0.001). We also observed significant improvements compared to Med-PaLM on every evaluation axis (p < 0.001) on newly introduced datasets of 240 long-form "adversarial" questions to probe LLM limitations. While further studies are necessary to validate the efficacy of these models in real-world settings, these results highlight rapid progress towards physician-level performance in medical question answering.
Data transmission between two or more digital devices in industry and government demands secure and agile technology. Digital information distribution often requires deployment of Internet of Things (IoT) devices and Data Fusion techniques which have also gained popularity in both, civilian and military environments, such as, emergence of Smart Cities and Internet of Battlefield Things (IoBT). This usually requires capturing and consolidating data from multiple sources. Because datasets do not necessarily originate from identical sensors, fused data typically results in a complex Big Data problem. Due to potentially sensitive nature of IoT datasets, Blockchain technology is used to facilitate secure sharing of IoT datasets, which allows digital information to be distributed, but not copied. However, blockchain has several limitations related to complexity, scalability, and excessive energy consumption. We propose an approach to hide information (sensor signal) by transforming it to an image or an audio signal. In one of the latest attempts to the military modernization, we investigate sensor fusion approach by investigating the challenges of enabling an intelligent identification and detection operation and demonstrates the feasibility of the proposed Deep Learning and Anomaly Detection models that can support future application for specific hand gesture alert system from wearable devices.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191