Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.
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The design process of centrifugal compressors requires applying an optimization process which is computationally expensive due to complex analytical equations underlying the compressor's dynamical equations. Although the regression surrogate models could drastically reduce the computational cost of such a process, the major challenge is the scarcity of data for training the surrogate model. Aiming to strategically exploit the labeled samples, we propose the Active-CompDesign framework in which we combine a thermodynamics-based compressor model (i.e., our internal software for compressor design) and Gaussian Process-based surrogate model within a deployable Active Learning (AL) setting. We first conduct experiments in an offline setting and further, extend it to an online AL framework where a real-time interaction with the thermodynamics-based compressor's model allows the deployment in production. ActiveCompDesign shows a significant performance improvement in surrogate modeling by leveraging on uncertainty-based query function of samples within the AL framework with respect to the random selection of data points. Moreover, our framework in production has reduced the total computational time of compressor's design optimization to around 46% faster than relying on the internal thermodynamics-based simulator, achieving the same performance.
Everyday life is increasingly influenced by artificial intelligence, and there is no question that machine learning algorithms must be designed to be reliable and trustworthy for everyone. Specifically, computer scientists consider an artificial intelligence system safe and trustworthy if it fulfills five pillars: explainability, robustness, transparency, fairness, and privacy. In addition to these five, we propose a sixth fundamental aspect: conformity, that is, the probabilistic assurance that the system will behave as the machine learner expects. In this paper, we propose a methodology to link conformal prediction with explainable machine learning by defining CONFIDERAI, a new score function for rule-based models that leverages both rules predictive ability and points geometrical position within rules boundaries. We also address the problem of defining regions in the feature space where conformal guarantees are satisfied by exploiting techniques to control the number of non-conformal samples in conformal regions based on support vector data description (SVDD). The overall methodology is tested with promising results on benchmark and real datasets, such as DNS tunneling detection or cardiovascular disease prediction.
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language equivalence (under the standard language valuation) for Kleene algebra terms, this coincidence is broken if we extend the terms with complements. In this paper, we prove the decidability of some fragments of the equational theory: the universality problem is coNP-complete, and the inequational theory t <= s is coNP-complete when t does not contain Kleene-star. To this end, we introduce words-to-letters valuations; they are sufficient valuations for the equational theory and ease us in investigating the equational theory w.r.t. languages. Additionally, we prove that for words with variable complements, the equational theory coincides with the word equivalence.
Everyday life is increasingly influenced by artificial intelligence, and there is no question that machine learning algorithms must be designed to be reliable and trustworthy for everyone. Specifically, computer scientists consider an artificial intelligence system safe and trustworthy if it fulfills five pillars: explainability, robustness, transparency, fairness, and privacy. In addition to these five, we propose a sixth fundamental aspect: conformity, that is, the probabilistic assurance that the system will behave as the machine learner expects. In this paper, we propose a methodology to link conformal prediction with explainable machine learning by defining CONFIDERAI, a new score function for rule-based models that leverages both rules predictive ability and points geometrical position within rules boundaries. We also address the problem of defining regions in the feature space where conformal guarantees are satisfied by exploiting techniques to control the number of non-conformal samples in conformal regions based on support vector data description (SVDD). The overall methodology is tested with promising results on benchmark and real datasets, such as DNS tunneling detection or cardiovascular disease prediction.
Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local, but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge--Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global, if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22($\alpha$) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22($\alpha$) schemes with nonnegative Runge-Kutta parameters.
Despite decades of research, developing correct and scalable concurrent programs is still challenging. Network functions (NFs) are not an exception. This paper presents NFork, a system that helps NF domain experts to productively develop concurrent NFs by abstracting away concurrency from developers. The key scheme behind NFork's design is to exploit NF characteristics to overcome the limitations of prior work on concurrency programming. Developers write NFs as sequential programs, and during runtime, NFork performs transparent parallelization by processing packets in different cores. Exploiting NF characteristics, NFork leverages transactional memory and develops efficient concurrent data structures to achieve scalability and guarantee the absence of concurrency bugs. Since NFork manages concurrency, it further provides (i) a profiler that reveals the root causes of scalability bottlenecks inherent to the NF's semantics and (ii) actionable recipes for developers to mitigate these root causes by relaxing the NF's semantics. We show that NFs developed with NFork achieve competitive scalability with those in Cisco VPP [16], and NFork's profiler and recipes can effectively aid developers in optimizing NF scalability.
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.
Whilst contrastive learning yields powerful representations by matching different augmented views of the same instance, it lacks the ability to capture the similarities between different instances. One popular way to address this limitation is by learning global features (after the global pooling) to capture inter-instance relationships based on knowledge distillation, where the global features of the teacher are used to guide the learning of the global features of the student. Inspired by cross-modality learning, we extend this existing framework that only learns from global features by encouraging the global features and intermediate layer features to learn from each other. This leads to our novel self-supervised framework: cross-context learning between global and hypercolumn features (CGH), that enforces the consistency of instance relations between low- and high-level semantics. Specifically, we stack the intermediate feature maps to construct a hypercolumn representation so that we can measure instance relations using two contexts (hypercolumn and global feature) separately, and then use the relations of one context to guide the learning of the other. This cross-context learning allows the model to learn from the differences between the two contexts. The experimental results on linear classification and downstream tasks show that our method outperforms the state-of-the-art methods.
Text-to-SQL is a task that converts a natural language question into a structured query language (SQL) to retrieve information from a database. Large language models (LLMs) work well in natural language generation tasks, but they are not specifically pre-trained to understand the syntax and semantics of SQL commands. In this paper, we propose an LLM-based framework for Text-to-SQL which retrieves helpful demonstration examples to prompt LLMs. However, questions with different database schemes can vary widely, even if the intentions behind them are similar and the corresponding SQL queries exhibit similarities. Consequently, it becomes crucial to identify the appropriate SQL demonstrations that align with our requirements. We design a de-semanticization mechanism that extracts question skeletons, allowing us to retrieve similar examples based on their structural similarity. We also model the relationships between question tokens and database schema items (i.e., tables and columns) to filter out scheme-related information. Our framework adapts the range of the database schema in prompts to balance length and valuable information. A fallback mechanism allows for a more detailed schema to be provided if the generated SQL query fails. Ours outperforms state-of-the-art models and demonstrates strong generalization ability on three cross-domain Text-to-SQL benchmarks.
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.
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