We study Galerkin model reduction for unconstrained linear-quadratic optimal control problems and show that state-space reduction alone already induces a reduced control structure via the optimality conditions. As a result, the solely state-reduced and the combined control- and state-reduced problems are equivalent, allowing fast optimization over a reduced control space without introducing additional approximation error. We derive lower and upper a posteriori error bounds for the optimal control and use them within an online-adaptive algorithm that constructs sufficiently accurate reduced spaces while solving the control problem. Convergence of the algorithm is proven, and numerical results demonstrate that combined control and state-space reduction yields significant speed-ups without loss of accuracy compared to state-space reduction alone.
Modeling multiphysics processes in porous media requires preconditioned iterative linear solvers to enable efficient simulations at industry-relevant scales. These solvers are typically composed of sub-algorithms that target individual physical processes. Various options are available for each algorithm, with the corresponding ranges of numerical parameters. The choices of sub-algorithms and their parameters significantly affect simulation performance and robustness. Optimizing these choices for each simulation is challenging due to the vast number of possible combinations. Moreover, optimization relies on performance data from past simulations, which becomes less representative as the simulation setup changes. This paper addresses the problem of automated selection and tuning of preconditioned linear solvers for multiphysics simulations, targeting a scenario where numerous linear systems of similar structure must be solved successively, generated by a single discretized set of equations. The proposed solver selection algorithm collects performance data during the run of the target simulation and continuously updates a machine learning model responsible for solver selection, resulting in an adaptively refined selection policy. The algorithm is evaluated on two time-dependent nonlinear model problems: (i) coupled fluid flow and heat transfer in porous media and (ii) thermo-poromechanics in porous media with fractures, governed by frictional contact mechanics. These experiments demonstrate that the algorithm selects efficient and robust solvers with negligible overhead and performs comparably to a reference selection policy that has full access to the performance data of prior simulations. Our results indicate that the proposed approach effectively addresses the challenge of solver selection and tuning, providing particular value to simulation engineers and researchers, especially when expert knowledge on linear solver tuning is not readily available.
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the success of deep neural networks and structured deep kernel networks, we consider deep, multilayer kernels for greedy approximation. This multilayer structure, consisting of linear kernel layers and optimizable kernel activation function layers in an alternating fashion, increases the expressiveness of the kernels and thus of the resulting approximants. Compared to standard kernels, deep kernels are able to adapt kernel intrinsic shape parameters automatically, incorporate transformations of the input space and induce a data-dependent reproducing kernel Hilbert space. For this, deep kernels need to be pretrained using a specifically tailored optimization objective. In this work, we not only introduce deep kernel greedy models, but also present numerical investigations and comparisons with neural networks, which clearly show the advantages in terms of approximation accuracies. As applications we consider the approximation of model problems, the prediction of breakthrough curves for reactive flow through porous media and the approximation of solutions for parameterized ordinary differential equation systems.
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter is high-dimensional, making computation of the posterior expensive due to the need to sample in a high-dimensional space and the need to evaluate an expensive high-dimensional forward model relating the unknown parameter to the data. However, inverse problems often exhibit low-dimensional structure due to the fact that the available data are only informative in a low-dimensional subspace of the parameter space. Dimension reduction approaches exploit this structure by restricting inference to the low-dimensional subspace informed by the data, which can be sampled more efficiently. Further computational cost reductions can be achieved by replacing expensive high-dimensional forward models with cheaper lower-dimensional reduced models. In this work, we propose new dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances, which arise in many practical inference settings. The dimension reduction approach is applicable to general linear Bayesian inverse problems whereas the model reduction approaches are specific to the problem of inferring the initial condition of a linear dynamical system. We provide theoretical approximation guarantees as well as numerical experiments demonstrating the accuracy and efficiency of the proposed approaches.
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard format. There are a number of open-source finite element libraries available, and it can be difficult to check that an implementation of an element in a library matches the element's definition in the literature or implementation in another library, especially when many libraries include variants of elements whose basis functions do not match exactly. In this paper, we carefully derive conditions under which elements can be considered equivalent and describe an algorithm that uses these conditions to verify that two implementations of a finite element are indeed variants of the same element. The results of scheduled runs of our implementation of this verification algorithm are included in the information available on DefElement.
Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional latent space. In this space, a linear pH system, that satisfies the pH properties per construction, is parameterized by the weights of a neural network. The mathematical requirements are met by defining the pH matrices through Cholesky factorizations. The neural networks that define the coordinate transformation and the pH system are identified in a joint optimization process to match the dynamics observed in the data while defining a linear pH system in the latent space. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size. The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example, as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.
In this paper, we extend the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et al. (J Comput Phys 393:465–483, 2019) and Nasab and Vermeire (J Comput Phys 468:111470, 2022) to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta methods we motivate a specific form of the Butcher arrays which leads to a family of fourth-order accurate methods. The employed form of the Butcher arrays results in a special structure of the stability polynomials, which needs to be adhered to for an efficient optimization of the domain of absolute stability. We demonstrate that the constructed fourth-order P-ERK methods satisfy linear stability, internal consistency, designed order of convergence, and conservation of linear invariants. At the same time, these schemes are seamlessly coupled for codes employing a method-of-lines approach, in particular without any modifications of the spatial discretization. We demonstrate speedup for single-threaded program executions, shared-memory parallelism, i.e., multi-threaded executions and distributed-memory parallelism with MPI. We apply the multirate P-ERK schemes to inviscid and viscous problems with locally varying wave speeds, which may be induced by non-uniform grids or multiscale properties of the governing partial differential equation. Compared to state-of-the-art optimized standalone methods, the multirate P-ERK schemes allow significant reductions in right-hand-side evaluations and wall-clock time, ranging from 66% up to factors greater than four. A reproducibility repository is provided which enables the reader to examine all results presented in this work.
Predictive modelling combining both numerical simulations and real-world measurement data, obtained from sensors, is gaining importance in computational science and engineering. Even with large-scale finite element models, a mismatch to the sensor data often remains, which can be attributed to different sources of uncertainty. For such a scenario, the statistical finite element method (statFEM) can be used to condition a simulated field on given sensor data. This yields a posterior solution which resembles the data much better and additionally provides consistent estimates of uncertainty, including model misspecification. For frequency or parameter dependent problems, occurring, e.g. in acoustics or electromagnetism, solving the full order model across the frequency range of interest and conditioning it on data quickly results in a prohibitive computational cost. In this case, the introduction of a surrogate in the form of a reduced order model (ROM) yields much smaller systems of equations. In this paper, we propose a reduced order statFEM framework relying on Krylov-based moment matching. We introduce a data model which explicitly includes the bias induced by the reduced approximation, which is estimated by an error indicator. The results of the new statistical reduced order method are compared to the standard statFEM procedure applied to a ROM prior without explicitly accounting for reduced order bias. The proposed method achieves better accuracy and faster convergence throughout a given frequency range for a variety of numerical examples and artificial (i.e. simulated) sensor data.
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry: (i) a variant of the coupled Benjamin-Bona-Mahony (BBM) equations and (ii) a recently proposed model by Svärd and Kalisch (2025) with enhanced dispersive behavior. Both models share the property of being conservative in terms of a nonlinear invariant, often interpreted as energy. This property is preserved exactly in our novel semidiscretizations. To obtain fully-discrete energy-stable schemes, we employ the relaxation method. Our novel methods generalize energy-conserving methods for the BBM-BBM system to variable bathymetries. Compared to the low-order, energy-dissipative finite volume method proposed by Svärd and Kalisch, our schemes are arbitrary high-order accurate, energy-conservative or -stable, can deal with periodic and reflecting boundary conditions, and can be any method within the framework of summation-by-parts operators including finite difference and finite element schemes. We present improved numerical properties of our methods in some test cases.
Overall, this app was created to solve the challenges of restaurant management [1]. We designed it to be simple and user-friendly for both managers and employees. Key features include secure authentication using Firebase, a weekly scheduling tool for managers, and an emergency contact feature to quickly find available employees [2]. Employees can manage their availability with a week-view calendar. The app's functionalities support check in check out updates for attendance and shift management, improving overall communication and coordination within the restaurant. To test its effectiveness, we surveyed managers and employees who used the app, receiving mostly positive feedback. Future updates will add direct messaging and inventory calculations within the app to incorporate more core features to the app. This app effectively boosts productivity and reduces miscommunication in restaurants, addressing common scheduling challenges and providing an solution. By focusing on enhancing communication and operational efficiency, our app aims to improve the restaurant management experience and efficiency.
This paper introduces "DanceWell," an app created to help dancers quickly get medical advice for injuries. The app was developed based on personal experiences and the difficulty of finding specialized care quickly and affordably. DanceWell uses artificial intelligence (AI) to analyze user input, such as symptoms and photos of injuries, to diagnose problems more accurately than traditional methods [1]. The app's main features include a photo upload tool for injury analysis and a set of yes/no questions tailored to each injury type. Experiments show that DanceWell can accurately provide medical advice, proving to be faster and more accessible than waiting for a doctor's appointment. The app makes it easier for dancers to get the right care quickly, allowing them to continue training and recover faster [2]. This project shows how AI can improve healthcare by providing specific, quick, and reliable support, suggesting that such technology should be used more widely.
Capturing aesthetically pleasing photographs can be challenging for amateur photographers due to the complexity of factors such as lighting, composition, and contrast. To address this issue, we propose a mobile application powered by deep learning models and regression analysis. This application analyzes real-time image frames using a pre-trained MobileNet backbone and a custom classification layer [8]. By leveraging the Aesthetics and Attributes database, the app calculates an aesthetic score for each photograph, providing instant feedback to users. Challenges encountered during development, including interfacing with machine learning models and implementing camera functionalities, are addressed. Through experiments, we evaluate different training approaches and compare our methodology with existing research. Our solution aims to empower users to capture high-quality photographs by assisting them in understanding and applying fundamental principles of photography.
I made this program so I can predict and deliver ESG scores of various companies to people [1]. I conducted an experiment to test out the accuracy of my sentiment determination system for posts and got about half correct. Three important systems in my program are the posting system, the authentication system, and the user interface. I used Scraper API to retrieve the posts l need for the posting system [2]. An alternative API is SmartProxy. I used Google Firebase for my authentication system [3]. Another one I could have used is Parse. I used Flutter to build the user interface system. An alternative is React Native.
The culinary industry, a vital component of the global economy, is increasingly challenged by job shortages and a resistance to automation. This paper addresses the growing tension between modernizing culinary practices through automation and preserving traditional cooking methods. To bridge this gap, we propose Auto Cook, a semi-automation tool that seamlessly integrates with existing kitchen infrastructure, enhancing efficiency without compromising the human touch in cooking. Auto Cook combines mechanical components, computational controls, and real-time data monitoring, enabling users to automate routine tasks while retaining creative control. Key challenges, such as adapting to diverse stove models, ensuring safety in hazardous kitchen environments, and managing power constraints, were effectively addressed through modular design, material innovation, and optimized power management. Experimental tests evaluated Auto Cook’s response to sudden temperature fluctuations, demonstrating its capability to stabilize conditions with minimal intervention. The results highlight Auto Cook as a practical, costeffective solution for modernizing kitchens, making it an essential tool for culinary professionals and enthusiasts alike.
Fuzzy logic provides a framework for dealing with uncertainty and imprecision, making it particularly useful in natural language processing (NLP) applications. A critical subset of fuzzy logic is fuzzy search, which enhances search capabilities by allowing approximate matches rather than requiring exact ones. This paper explores the integration of fuzzy search techniques within the context of wholesale pharma distribution, a field that demands high accuracy in data retrieval due to its impact on public health and safety.We investigate two distinct case studies where each demonstrates specific fuzzy search techniques tailored to address unique challenges in data retrieval. Through a Python code implementation, we illustrate how these techniques can be practically applied to improve the accuracy and efficiency of searches within large datasets common in wholesale pharma distribution environments. Our findings underscore the potential of fuzzy logic as a transformative tool for enhancing information retrieval systems.By providing practical insights and technical guidance, this research aims to empower stakeholders in the pharmaceutical industry to leverage fuzzy search techniques effectively, ultimately contributing to better data management practices and improved decision-making processes.
In this vision paper, we thoroughly explore the potential of integrating artificial intelligence (AI) solutions into software product lines (SPLs) to overcome challenges like scalability and complexity. By harnessing AI's machine learning and automation capabilities, SPLs can significantly enhance feature selection, variability management, and customization. We uncover foundational concepts, expected benefits, and future research directions for AI-driven SPLs, including scalable machine learning, adaptive variability management, real-time adaptation and personalized customization. Our aim is to stimulate innovation and foster discussion in the software engineering community, driving towards more efficient, adaptable, and user-friendly software systems. The integration of AI into SPLs represents a fundamental shift in software development, promising improvements in productivity, quality, and user satisfaction.
Sometimes people want to learn the dance of their favorite celebrity, but they often fail to notice the details when learning by themselves, my application helps users to find the details that they fail to notice and point them out, during the development process I encountered the problem of where to start analyzing the video when the length of the video is different between the user and the professional, and what to do when the computer calculates the angle of the error, I applied Machine Learning K- Means clustering and change the formula to solve the problem, he is worth using because some dancers want to improve their dancing level and ability [1].
This paper introduces the Utrip app, explaining various functions and the codes involved in this app. We solved problems like music recommendations and AI chatbox, making sure that they ran without getting errors [1]. So, the user can use it to enhance their travel experience. One of the problems that we encounter is that the GPT model we used does not naturally return a JSON format for our app to read [2]. Therefore, we need to engineer our prompt to specifically ask for a response in a designated JSON format, and parse the response string to convert it to JSON. In our experiment, we tested out the rate of error while using different prompt formats for the GPT model [3]. We found out that the prompt that specifies a JSON format in English words is the best. We also compared our app to ones made by others. Our app allows users to create their own travel plans, and the AI chatbox provides suitable suggestions based on real-time scenarios.
Cyber-Physical Systems (CPS) integrate physical and embedded systems with information and communication technology systems, monitoring and controlling physical processes with minimal human intervention. The connection to information and communication technology exposes CPS to cyber risks. It is crucial to assess these risks to manage them effectively. This paper reviews scholarly contributions to cyber risk assessment for CPS, analyzing how the assessment approaches were evaluated and investigating to what extent they meet the requirements of effective risk assessment. We identify gaps limiting the effectiveness of the assessment and recommend real-time learning from cybersecurity incidents. Our review covers twenty-eight papers published between 2014 and 2023, selected based on a three-step search. Our findings show that the reviewed cyber risk assessment methodologies revealed limited effectiveness due to multiple factors. These findings provide a foundation for further research to explore and address other factors impacting the quality of cyber risk assessment in CPS.
