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We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa's (global) RBF method. We give the estimates in the discrete l(2)-norm 2-norm intrinsic to each of the three methods. The results show that Kansa's method and RBF-PUM can be l(2)-stable 2-stable in time under a sufficiently large oversampling of the discretized system of equations. The RBF-FD method in addition requires stabilization of the spurious jump terms due to the discontinuous RBF-FD cardinal basis functions. Numerical experiments show an agreement with our theoretical observations.

In many areas of data-driven science, large datasets are generated where the individual data objects are images, matrices, or otherwise have a clear structure. However, these objects can be information-sparse, and a challenge is to efficiently find and work with the most interesting data as early as possible in an analysis pipeline. We have recently proposed a new model for big data management where the internal structure and information of the data are associated with each data object (as opposed to simple metadata). There is then an opportunity for comprehensive data management solutions to account for data-specific internal structure as well as access patterns. In this article, we explore this idea together with our recently proposed hierarchical storage management framework that uses reinforcement learning (RL) for autonomous and dynamic data placement in different tiers in a storage hierarchy. Our case-study is based on four scientific datasets: Protein translocation microscopy images, Airfoil angle of attack meshes, 1000 Genomes sequences, and Phenotypic screening images. The presented results highlight that our framework is optimal and can quickly adapt to new data access requirements. It overall reduces the data processing time, and the proposed autonomous data placement is superior compared to any static or semi-static data placement policies.

Under appropriate technical assumptions, the simple-loop theory allows to derive various types of asymptotic expansions for the eigenvalues of Toeplitz matrices generated by a function f. Unfortunately, such a theory is not available in the preconditioning setting, that is for matrices of the form with real-valued, g nonnnegative and not identically zero almost everywhere. Independently and under the milder hypothesis that is even and monotonic over , matrix-less algorithms have been developed for the fast eigenvalue computation of large preconditioned matrices of the type above, within a linear complexity in the matrix order: behind the high efficiency of such algorithms there are the expansions as in the case , combined with the extrapolation idea, and hence we conjecture that the simple-loop theory has to be extended in such a new setting, as the numerics strongly suggest. Here we focus our attention on a change of variable, followed by the asymptotic expansion of the new variable, and we consider new matrix-less algorithms ad hoc for the current case. Numerical experiments show a much higher accuracy till machine precision and the same linear computational cost, when compared with the matrix-less procedures already proposed in the literature.

Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often makes more visible the non-associativity impact in floating-point operations. These problems are even amplified when communication-hiding pipelined algorithms are used to improve the parallelization of Krylov subspace methods. Introducing reproducibility in the implementations avoids these problems by getting more robust and correct solutions. This paper proposes a general framework for deriving reproducible and accurate variants of Krylov subspace methods. The proposed algorithmic strategies are reinforced by programmability suggestions to assure deterministic and accurate executions. The framework is illustrated on the preconditioned BiCGStab method and its pipelined modification, which in fact is a distinctive method from the Krylov subspace family, for the solution of non-symmetric linear systems with message-passing. Finally, we verify the numerical behavior of the two reproducible variants of BiCGStab on a set of matrices from the SuiteSparse Matrix Collection and a 3D Poisson’s equation., eSSENCE - An eScience Collaboration

Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order O(n^(-4)) with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency.

It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non-Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non-Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix-size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects; for example, non-Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high-precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.

The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few years. However, even if its convergence and stability are now established both in the continuous and discrete setting, it is still an open problem to understand up to what extent this approach can separate two close-by frequencies contained in a signal.In this paper, first we recall previously discovered theoretical results about Iterative Filtering. Afterward, we prove a few new theorems regarding the ability of this method in separating two nearby frequencies both in the case of continuously and discrete sampled signals. Among them, we prove a theorem which allows to construct filters which captures, up to machine precision, a specific frequency. We run numerical tests to confirm our findings and to compare the performance of Iterative Filtering with the one of Empirical Mode Decomposition and Synchrosqueezing methods. All the results presented confirm the ability of the technique under investigation in addressing the fundamental "one or two frequencies" question.

This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a highorder finite element method with an invariant-domain preserving low-order method that uses the closest neighbor stencil. The construction of the flux of the low-order method is based on an idea from Abgrall et al. (2017). The mass flux of the low-order and the high-order methods are identical on each finite element cell. This allows for mass preserving and invariant-domain preserving limiting.

We study the hydrodynamic interaction between a microswimmer and a deformable interface when the swimmer can stochastically reorient itself. We consider a force- and torque-free swimmer, modeled as a slender body, that can execute random orientation tumbles or active Brownian rotations in the plane of the deformable interface. When the swimmer is in the more viscous fluid, our analysis shows that both tumbles and Brownian rotations acting on timescales comparable to that of interface deformations can lead to a pusher-type swimmer rotating away from the interface, while enhancing its attraction towards the interface. In turn, the intrinsic orientational stochasticity of the microswimmer favors a stronger migration of pushers towards the interface at short times, but migration away from the interface in the long-time limit. However, irrespective of the viscosity ratio of the two fluid medium, the tendency of a pusher to align parallel to the interface is suppressed; the results for puller-type swimmers are the opposite. Our study has potential consequences for the residence time of swimming microorganisms near deformable boundaries., QC 20240318

In this article, we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (nonquadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and nonquadratic problems., QC 20240118

Since its inception, isogeometric analysis (IGA) has shown significant advantages over Lagrange polynomials-based finite element analysis (FEA), especially for contact problems. IGA often uses C1-continuous non-uniform rational B-splines (NURBS) as basis functions, providing a smooth description of kinematic variables across the contact interface. This leads to increased accuracy and stability in the numerical solutions. However, from the existing literature on isogeometric contact analysis, it is not yet clear what interpolation order and continuity of NURBS one should employ to accurately capture the distribution of contact forces across the contact interface. The present work aims to fill this gap and provides a comparative assessment of different NURBS-based standard (conventional) refinement strategies for contact problems within the IGA framework. A recently proposed refinement strategy, known as the varying-order (VO) based NURBS discretization, has demonstrated its capability to refine geometry through the implementation of order elevation in a controlled manner. However, a detailed investigation that directly compares the VO based NURBS discretization with the standard NURBS discretization has not yet been carried out. Therefore, a thorough study of the VO based discretization strategy is also conducted, evaluating its effectiveness in comparison with the standard discretization strategy for contact problems. For this, a few examples on contact problems are solved using an in-house MATLAB® code. The solution to these examples shows that quadratic order standard NURBS discretization is sufficient to achieve the desired level of solution accuracy just by increasing the mesh size. It is further demonstrated that VO based discretization can achieve much higher accuracy than standard discretization, even with a coarse mesh, by generating additional degrees of freedom in the contact boundary layer. In addition, VO based discretization makes considerable savings i, QC 20240318

The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell (PIC) methods owing to its ease of implementation and favorable scalability in high-dimensional problems. An unfortunate drawback of the method is the introduction of statistical noise resulting from the use of finitely many particles. In this paper we examine the application of the Smoothness-Increasing Accuracy-Conserving (SIAC) family of convolution kernel filters as denoisers for moment data arising from PIC simulations. We show that SIAC filtering is a promising tool to denoise PIC data in the physical space as well as capture the appropriate scales in the Fourier space. Furthermore, we demonstrate how the application of the SIAC technique reduces the amount of information necessary in the computation of quantities of interest in plasma physics such as the Bohm speed., QC 20240305

Rigid particles in a Stokesian fluid experience an increasingly strong lubrication resistance as particle gaps narrow. Numerically, resolving these lubrication forces comes at an intractably large cost, even for moderate system sizes. Hence, it can typically not be guaranteed that artificial particle collisions and overlaps do not occur in a dynamic simulation, independently of the choice of method to solve the Stokes equations. In this work, the potentially large set of non-overlap constraints, in terms of the Euclidean distance between boundary points on disjoint particles, are efficiently represented via a barrier energy. We solve for the minimum magnitudes of repelling contact forces and torques between any particle pair in contact to correct for overlaps by enforcing a zero barrier energy at the next time level, given a contact-free configuration at a previous instance in time. Robustness for the method is illustrated using a multiblob method to solve the mobility problem in Stokes flow, applied to suspensions of spheres, rods and boomerang shaped particles. Collision free configurations are obtained at all instances in time, and considerably larger time-steps can be taken than without the technique. The effect of the contact forces on the collective order of a set of rods in a background flow that naturally promote particle interactions is also illustrated., QC 20231205

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.

Algorithms designed to solve dynamic multi-objective optimization problems (DMOPs) need to consider all of themultiple conflicting objectives to determine the optimal solutions. However, objective functions, constraints orparameters can change over time, which presents a considerable challenge. Algorithms should be able not only toidentify the optimal solution but also to quickly detect and respond to any changes of environment. In order toenhance the capability of detection and response to environmental changes, we propose a dynamic multiobjectiveoptimization (DMOO) algorithm based on the detection of environment change intensity andensemble learning (DMOO-DECI&EL). First, we propose a method for detecting environmental change intensity,where the change intensity is quantified and used to design response strategies. Second, a series of responsestrategies under the framework of ensemble learning are given to handle complex environmental changes.Finally, a boundary learning method is introduced to enhance the diversity and uniformity of the solutions.Experimental results on 14 benchmark functions demonstrate that the proposed DMOO-DECI&EL algorithmachieves the best comprehensive performance across three evaluation criteria, which indicates that DMOODECI&EL has better robustness and convergence and can generate solutions with better diversity compared tofive other state-of-the-art dynamic prediction strategies. In addition, the application of DMOO-DECI&EL to thereal-world scenario, namely the economic power dispatch problem, shows that the proposed method caneffectively handle real-world DMOPs.

We establish the existence of a weak solution for a strongly coupled, nonlinear Stokes–Maxwell system, originally proposed by Nika and Vernescu (Z Angew Math Phys71(1):1–19, 2020) in the three-dimensional setting. The model effectively couplesthe Stokes equation with the quasi-static Maxwell’s equations through the Lorentzforce and the Maxwell stress tensor. The proof of existence is premised on: (i) theaugmented variational formulation of Maxwell’s equations, (ii) the definition of a newfunction space for the magnetic induction and the verification of a Poincar’e-typeinequality, and (iii) the deployment of the Altman–Shinbrot fixed point theorem whenthe magnetic Reynolds number, Rm, is small.

Collections of time series formed via aggregation are prevalent in many fields. These are commonly referred to as hierarchical time series and may be constructed cross-sectionally across different variables, temporally by aggregating a single series at different frequencies, or even generalised beyond aggregation as time series that respect linear constraints. When forecasting such time series, a desirable condition is for forecasts to be coherent: to respect the constraints. The past decades have seen substantial growth in this field with the development of reconciliation methods that ensure coherent forecasts and improve forecast accuracy. This paper serves as a comprehensive review of forecast reconciliation and an entry point for researchers and practitioners dealing with hierarchical time series. The scope of the article includes perspectives on forecast reconciliation from machine learning, Bayesian statistics and probabilistic forecasting, as well as applications in economics, energy, tourism, retail demand and demography., CC BY 4.0 DEED© 2023 The Author(s)Available online 29 December 2023Correspondence Address: G. Athanasopoulos; Monash University, VIC, 3145, Australia; email: george.athanasopoulos@monash.edu; CODEN: IJFOEWe thank Tommaso Di Fonzo, Xiaoqian Wang and Daniele Girolimetto for providing helpful comments onan earlier draft of this paper. Rob J Hyndman was funded by the Australian Government through the Australian Research Council Industrial Transformation Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA), Project ID IC200100009.

The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were extended to multicomponent monatomic gases and polyatomic single species. For multicomponent polyatomic gases, the case where the polyatomicity is modelled by a discrete internal energy variable was considered lately. Here we consider the corresponding case for a continuous internal energy variable. Compactness results, stating that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a decomposition, such that the terms are, or at least are uniform limits of, Hilbert-Schmidt integral operators and therefore are compact operators. Moreover, bounds on-including coercivity of-the collision frequency are obtained for hard sphere like, as well as hard potentials with cutoff like, models, from which Fredholmness of the linearized collision operator follows, as well as its domain.

An approximate computational model of an electromagnetic (EM) pulse excited thin-wire antenna is developed. The presented solution methodology is based on the Cagniard-deHoop method of moments (CdH-MoM) and Hallén's approximation of the thin-wire model. It is shown that the proposed time-domain (TD) solution leads to an inversion-free, efficient updating procedure that mitigates the marching-on-in-time accumulation error. An illustrative numerical example demonstrates the validity of the proposed model., Validerad;2024;Nivå 2;2024-03-18 (hanlid);Full text license: CC BY

We investigate the influence of uncertain data on solutions to initial boundary value problems with well posed boundary conditions. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for short and long time calculations. For short time calculations, uncertainty in the initial data dominates. As time grows, the influence of initial data vanishes exponentially fast. For longer time calculations, the uncertainty in the forcing function and boundary data dominate, as they grow in time. Errors due to the forcing function grow faster (linearly in time) than the ones due to the boundary data (grow as the square root of time). Roughly speaking, the results indicate that for short time calculations, the initial conditions are the most important, but for longer time calculations, focus should be on the forcing function and boundary conditions. The findings are especially important when similar mathematical and numerical techniques are used for both short and long times. Our qualitative results can guide more quantitative investigations where details of the uncertain data are known., Funding Agencies|Vetenskapsradet, Sweden [2021-05484 VR]; University of Johannesburg

The presented work addresses two-stage stochastic programs (2SPs), a broadly applicable model to capture optimization problems subject to uncertain parameters with adjustable decision variables. In case the adjustable or second-stage variables contain discrete decisions, the corresponding 2SPs are known to be NP-complete. The standard approach of forming a single-stage deterministic equivalent problem can be computationally challenging even for small instances, as the number of variables and constraints scales with the number of scenarios. To avoid forming a potentially huge MILP problem, we build upon an approach of approximating the expected value of the second-stage problem by a neural network (NN) and encoding the resulting NN into the first-stage problem. The proposed algorithm alternates between optimizing the first-stage variables and retraining the NN. We demonstrate the value of our approach with the example of computing operating points in power systems by showing that the alternating approach provides improved first-stage decisions and a tighter approximation between the expected objective and its neural network approximation., QC 20240314 Part of ISBN 9783031539657

A novel method to calculate single-particle fabric tensors and related geometric characteristics (contact, free and particle area, particle volume and contact centroid) of assemblies of spherical particles has been developed. A standard contact detection stage is used to identify overlapping particles. The shape of each contact region is obtained as the intersection of a circle, obtained in the absence of any contact impingement, and a convex polygon, determined by halfplane intersection based on directed lines obtained from the intersection of contact planes. An underlying power diagram is used to subdivide volume and area between particles, but calculations are performed particle-wise, resulting in an efficient algorithm with a structure ideally suited for parallelisation. Numerical tests performed on loose and dense particle assemblies and comparison (of single-particle free area and particle volume) with a reference method (POWERSASA) indicate that the method is robust and highly accurate. The method will be useful not only for geometric analysis but also as a basis for subsequent developments of strain measures and computational procedures for highly deformed granular materials. Moreover, it constitutes a viable alternative for calculation of solvent accessible surface areas, considering its robustness, efficiency and ease of parallelisation.

One of the most fundamental problems in simultaneous localization and mapping (SLAM) is the ability to take into account data association (DA) uncertainties. In this article, this problem is addressed by proposing a multihypotheses sampling distribution for particle filtering-based SLAM algorithms. By modeling the measurements and landmarks as random finite sets, an importance density approximation that incorporates DA uncertainties is derived. Then, a tractable Gaussian mixture model approximation of the multihypotheses importance density is proposed, in which each mixture component represents a different DA. Finally, an iterative method for approximating the mixture components of the sampling distribution is utilized and a partitioned update strategy is developed. Using synthetic and experimental data, it is demonstrated that the proposed importance density improves the accuracy and robustness of landmark-based SLAM in cluttered scenarios over state-of-the-art methods. At the same time, the partitioned update strategy makes it possible to include multiple DA hypotheses in the importance density approximation, leading to a favorable linear complexity scaling, in terms of the number of landmarks in the field-of-view.

Generalized adaptive feedforward cancellation with a reference sensor is considered to specifically suppress second harmonic torque oscillations with an ac fed propulsion system for an electric train. A single complex-valued design parameter is tracked through gradient-type adaptation. Both Cartesian and polar parameter representations are considered, resulting in quite varying convergence properties. Three different adaptation algorithms are proposed and evaluated using power lab experiments. At fixed operating conditions, a Cartesian form parameter adaptation is shown to be more robust to the choice of initial conditions, whereas a polar form representation shows better performance when covering a wide range of operating points., QC 20240307

We present an entropy stable nodal discontinuous Galerkin spectral element method (DGSEM) for the two-layer shallow water equations on two dimensional curvilinear meshes. We mimic the continuous entropy analysis on the semi-discrete level with the DGSEM constructed on Legendre–Gauss–Lobatto (LGL) nodes. The use of LGL nodes endows the collocated nodal DGSEM with the summation-by-parts property that is key in the discrete analysis. The approximation exploits an equivalent flux differencing formulation for the volume contributions, which generate an entropy conservative split-form of the governing equations. A specific combination of a numerical surface flux and discretization of the nonconservative terms is then applied to obtain a high-order path-conservative scheme that is entropy conservative. Furthermore, we find that this combination yields an analogous discretization for the pressure and nonconservative terms such that the numerical method is well-balanced for discontinuous bathymetry on curvilinear domains. Dissipation is added at the interfaces to create an entropy stable approximation that satisfies the second law of thermodynamics in the discrete case, while maintaining the well-balanced property. We conclude with verification of the theoretical findings through numerical tests and demonstrate results about convergence, entropy stability and well-balancedness of the scheme., Funding: Linköping University; Vetenskapsradet, Sweden; Swedish Research Council [2020-03642 VR]; [2022-06725]

In this work, we are interested in solving large linear systems stemming from the extra-membrane-intra model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial differential equations equipped with proper boundary conditions, we provide its finite element discretization and focus on the resulting large linear systems. We first give a relatively complete spectral analysis using tools from the theory of Generalized Locally Toeplitz matrix sequences. The obtained spectral information is used for designing appropriate preconditioned Krylov solvers. Through numerical experiments, we show that the presented solution strategy is robust w.r.t. problem and discretization parameters, efficient and scalable.

The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace–Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.

While a big wave of artificial intelligence (AI) has propagated to the field of computational fluid dynamics (CFD) acceleration studies, recent research has highlighted that the development of AI techniques that reconciles the following goals remains our primary task: (1) accurate prediction of unseen (future) time series in long-term CFD simulations (2) acceleration of simulations (3) an acceptable amount of training data and time (4) within a multiple PDEs condition. In this study, we propose a residual-based physics-informed transfer learning (RePIT) strategy to achieve these four objectives using ML-CFD hybrid computation. Our hypothesis is that long-term CFD simulation is feasible with the hybrid method where CFD and AI alternately calculate time series while monitoring the first principle's residuals. The feasibility of RePIT strategy was verified through a CFD case study on natural convection. In a single training approach, a residual scale change occurred around 100th timestep, resulting in predicted time series exhibiting non-physical patterns as well as a significant deviations from the ground truth. Conversely, RePIT strategy maintained the residuals within the defined range and demonstrated good accuracy throughout the entire simulation period. The maximum error from the ground truth was below 0.4 K for temperature and 0.024 m/s for x-axis velocity. Furthermore, the average time for 1 timestep by the ML-GPU and CFD-CPU calculations was 0.171 s and 0.015 s, respectively. Including the parameter-updating time, the simulation was accelerated by a factor of 1.9. In conclusion, our RePIT strategy is a promising technique to reduce the cost of CFD simulations in industry. However, more vigorous optimization and improvement studies are still necessary., QC 20231218

A new Grey-Area Mitigation (GAM) method for hybrid RANS-LES is presented., QC 20231214

Complementing large-eddy simulation (LES) with wall-modelling is, perhaps, the most straight-forward way to enable high-fidelity simulations at high Reynolds numbers. At the same time, high-order methods offer the benefits of high computational efficiency and potentially faster convergence with respect to mesh refinement even outside the asymptotic regime., QC 20231214

In this contribution, we present a robust and efficient computational framework capable of accurately capturing the dynamic motion and large deformation/deflection responses of highly-flexible rods interacting with an incompressible viscous flow. Within the partitioned approach, we adopt separate field solvers to compute the dynamics of the immersed structures and the evolution of the flow field over time, considering finite Reynolds numbers. We employ a geometrically exact, nonlinear Cosserat rod formulation in the context of the isogeometric analysis (IGA) technique to model the elastic responses of each rod in three dimensions (3D). The Navier–Stokes equations are resolved using a pressure projection method on a standard staggered Cartesian grid. The direct-forcing immersed boundary method is utilized for coupling the IGA-based structural solver with the finite-difference fluid solver. In order to fully exploit the accuracy of the IGA technique for FSI simulations, the proposed framework introduces a new procedure that decouples the resolution of the structural domain from the fluid grid. Uniformly distributed Lagrangian markers with density relative to the Eulerian grid are generated to communicate between Lagrangian and Eulerian grids consistently with IGA. We successfully validate the proposed computational framework against two- and three-dimensional FSI benchmarks involving flexible filaments undergoing large deflections/motions in an incompressible flow. We show that six times coarser structural mesh than the flow Eulerian grid delivers accurate results for classic benchmarks, leading to a major gain in computational efficiency. The simultaneous spatial and temporal convergence studies demonstrate the consistent performance of the proposed framework, showing that it conserves the order of the convergence, which is the same as that of the fluid solver., QC 20231031

Zeroth-order optimization has become increasingly important in complex optimization and machine learning when cost functions are impossible to be described in closed analytical forms. The key idea of zeroth-order optimization lies in the ability for a learner to build gradient estimates by queries sent to the cost function, and then traditional gradient descent algorithms can be executed replacing gradients by the estimates. For optimization over large-scale multi-agent systems with decentralized data and costs, zeroth-order optimization can continue to be utilized to develop scalable and distributed algorithms. In this paper, we aim at understanding the trend in performance transitioning from centralized to distributed zeroth-order algorithms in terms of convergence rates, and focus on multi-agent systems with time-varying communication networks. We establish a series of convergence rates for distributed zeroth-order subgradient algorithms under both one-point and two-point zeroth-order oracles. Apart from the additional node-to-node communication cost due to the distributed nature of algorithms, the established rates in convergence are shown to match their centralized counterpart. We also propose a multi-stage distributed zeroth-order algorithm that better utilizes the learning rates, reduces the computational complexity, and attains even faster convergence rates for compact decision set., QC 20231113

Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial differential equations, only a few stability results are known. In particular, if boundary conditions are included, stability issues frequently occur. The question we address in this paper is how provable stability for RBF methods can be obtained. We develop a stability theory for global radial basis function methods using the general framework of summation-by-parts operators often used in the Finite Difference and Finite Element communities. Although we address their practical construction, we restrict the discussion to basic numerical simulations and focus on providing a proof of concept., Funding agencies; Open Access funding enabled and organized by Projekt DEAL. JG was supported by AFOSR #F9550-18-1-0316 and ONR MURI #N00014-20-1-2595. JN was supported by Vetenskapsrådet, Sweden grant 2018-05084 VR and 2021-05484 VR, and the University of Johannesburg. PÖ was supported by the Gutenberg Research College, JGU Mainz.

We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in skew-symmetric form, including dissipative terms. The complete procedure has two main ingredients. Firstly, the energy rate in terms of a surface integral with boundary terms is derived. Secondly, we bound the surface integral by deriving new nonlinear boundary procedures for boundary conditions with non-zero data. The new nonlinear boundary procedure generalises the well known characteristic boundary procedure for linear problems to the nonlinear setting. To introduce the procedure, a skew-symmetric scalar IBVP encompassing the linear advection equation and Burgers equation is analysed. Once the continuous analysis is done, we show that energy stable nonlinear discrete approximations follow by using summation-by-parts operators combined with weak boundary conditions. The scalar analysis is subsequently repeated for general nonlinear systems of equations. Finally, the new boundary procedure is applied to four important IBVPs in computational fluid dynamics: the incompressible Euler and Navier-Stokes, the shallow water and the compressible Euler equations., Funding: Vetenskapsradet, Sweden [2021-05484 VR]; University of Johannesburg

We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable coefficient initial boundary value problems can be formulated in simple and straightforward ways using high-order accurate operators of generalized summation-by-parts type. Encapsulated features on a single computational block or element may include polynomial bases, tensor products as well as curvilinear coordinate transformations. Moreover, through the use of inner product preserving interpolation or projection, the global summation-by-parts property is extended to arbitrary multi-block or multi-element meshes with non-conforming nodal interfaces.

Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order initial value problems (IVPs). By discretizing the dynamics along a world-line parameter, instead of physical time directly, we retain manifest translation symmetry and conservation of the associated continuum Noether charge. A non-equidistant time discretization emerges dynamically, realizing a form of automatic adaptive mesh refinement (AMR), guided by the system symmetries. Using appropriately regularized summation by parts finite difference operators, the continuum Noether charge, defined via the Killing vector associated with translation symmetry, is shown to be exactly preserved in the interior of the simulated time interval. The convergence properties of the approach are demonstrated with two explicit examples., Funding: Research Council ofNorway under the FRIPRO Young Research Talent grant [286883]; Swedish Research Council [2021-05484]; UNINETT Sigma2-the National Infrastructure for High Performance Computing and Data Storage in Norway

In this paper, we introduce a high-order accurate finite element method for incompressible variable density flow. The method uses high-order Taylor-Hood velocity-pressure elements in space and backward differentiation formula (BDF) time stepping in time. This way of discretization leads to two main issues: (i) a saddle point system that needs to be solved at each time step; a stability issue when the viscosity of the flow goes to zero or if the density profile has a discontinuity. We address the first issue by using Schur complement preconditioning and artificial compressibility approaches. We observed similar performance between these two approaches. To address the second issue, we introduce a modified artificial Guermond-Popov viscous flux where the viscosity coefficients are constructed using a newly developed residual-based shock-capturing method. Numerical validations confirm high-order accuracy for smooth problems and accurately resolved discontinuities for problems in 2D and 3D with varying density ratios.

Polyurethane (PU) possesses excellent thermal properties, making it an ideal material for thermal insulation. Incorporating Phase Change Materials (PCMs) capsules into Polyurethane has proven to be an effective strategy for enhancing building envelopes. This innovative design substantially enhances indoor thermal stability and minimizes fluctuations in indoor air temperature. To investigate the thermal conductivity of the Polyurethane-Phase Change Materials foam composite, we propose a hierarchical multi-scale model utilizing Physics-Informed Neural Networks (PINNs). This model allows accurate prediction and analysis of the material’s thermal conductivity at both the meso-scale and macro-scale. By leveraging the integration of physics-based knowledge and data-driven learning offered by Physics-Informed Neural Networks, we effectively tackle inverse problems and address complex multi-scale phenomena. Furthermore, the obtained thermal conductivity data facilitates the optimization of material design. To fully consider the occupants’ thermal comfort within a building envelope, we conduct a case study evaluating the performance of this optimized material in a detached house. Simultaneously, we predict the energy consumption associated with this scenario. All outcomes demonstrate the promising nature of this design, enabling passive building energy design and significantly improving occupants’ comfort. The successful development of this Physics-Informed Neural Networks-based multi-scale model holds immense potential for advancing our understanding of Polyurethane-Phase Change Material’s thermal properties. It can contribute to the design and optimization of materials for various practical applications, including thermal energy storage systems and insulation design in advanced building envelopes.

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modeling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modeled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element., The first author is thankful for the financial support given by UCLouvain.

The thesis proposes to model the flow of gases in a room by solving the incompressible Navier-Stokes equations in three dimensions. The transportationof scalars such as temperature and concentration of CO2 is modeled by solving the advection-diffusion equation, and the effects of temperature on thevelocity is accounted for by employing the Boussinesq approximation. Theequations are solved numerically in Matlab by using the finite volume methodon a cubic domain with Cartesian coordinates. The code is verified by comparison with the well studied case of a lid-driven cavity. Different boundaryconditions are discussed and boundary conditions to model inlets and outlets along with radiators and windows are proposed. A simplified model of aroom is created and is shown to provide reasonable results for low Reynoldsnumbers (Re ≈ 200). It is also shown that the model is not efficient enoughto run simulations with higher Reynolds numbers (Re ≈ 20000) that resultfrom a realistic choice of parameters.Teknisk-naturvetenskapliga fakult

This project aims to develop a simulator for generating realistic data from vehicles operating in underground mines, encompassing positional data and sensor values of the velocity and angle. The project addresses the challenge of analyzing the Hybrid Positioning algorithm within Mobilaris Onboard, a navigation system for underground mines. The absence of the 100% ground truth for vehicle positions in the post-analysis of sensor log files necessitates the creation of this simulator. The project's mission includes generating vehicle paths and corresponding sensor readings, focusing on realism. Additional considerations include introducing realistic noise and integrating the simulator's output with visualization tools. Furthermore, the project aims to develop a tool for comparing simulated sensor values with actual sensor data, facilitating algorithm refinement and development. The project also incorporates time series analysis to interpret the sensor data generated by the simulator. This approach is crucial for understanding patterns and trends in the vehicle's positional and velocity data over time, providing valuable insights for refining the navigation algorithm.

Magnetic Resonance Imaging (MRI) is an essential healthcare technology, with diffusion MRI being a specialized technique. Diffusion MRI exploits the inherent diffusion of water molecules within the human body to produce a high-resolution tissue image. An MRI image contains information about a 3D volume in space, composed of 3D units called voxels. This thesis assumes the existence of a probability distribution for the diffusivity within a voxel, the diffusion tensor distribution (DTD), with the diffusivity described by a family of diffusion tensors. In 2D, these tensors can be described by 2x2 symmetric positive semidefinite matrices. The objective is to estimate the DTD of a voxel with neural networks for both 1D and 2D diffusion tensors. We assume the DTD to be a discrete distribution, with a finite set of diffusion tensors. The MRI signal is influenced by several experimental parameters, which for diffusion measurements are summarized in the measurement tensor B. To determine the diffusivity of a voxel, multiple measurement tensors are utilized, producing various MRI signals. From these signals, the network estimates the corresponding DTD of the voxel. The network seeks to employ the earth mover's distance (EMD) as its loss function, given the established use of EMD as a distance between probability distributions. Due to the difficulty of expressing the EMD as a differentiable loss function, the Sinkhorn distance, an entropic regularized approximation of the EMD, is used instead. Different network configurations are explored through simulations to identify optimal settings, assessed by the EMD loss and the closeness of the Sinkhorn loss to the EMD. The results indicate that the network achieves satisfactory accuracy when approximating DTDs with a small number of diffusivities, but struggles when the number increases. Future work could explore alternative loss functions and advanced neural network architectures. Despite the challenges encountered, this thesis offe

This paper examines the structural, thermodynamic, dynamic, elastic, and electronic properties of doped 2D diamond C4X2 (X = B or N) nanosheets in both AA ' A '' and ABC stacking configurations, by first-principles calculations. Those systems consist of three diamond-like graphene sheets with an undoped graphene layer between two 50% doped ones. Our results, based on the analysis of ab initio molecular dynamics simulations, phonon dispersion spectra, and Born's criteria for mechanical stability, revealed that all four structures are stable. Additionally, their standard enthalpy of formation values are similar to that of pristine 2D diamonds, recently synthesized by compressing three graphene layers together. The C4X2 (X = B or N) systems exhibit high elastic constant values and stiffness comparable to that of bulk diamond. The C4N2 nanosheets present wide indirect band gaps that could be advantageous for applications similar to those of the hexagonal boron nitride (h-BN), such as a substrate for high-mobility 2D devices. On the other hand, the C4B2 systems are semiconductors with direct band gaps, in the 1.6-2.0 eV range, and small effective masses, which are favorable characteristics to high carrier mobility and optoelectronics applications.

We present theory for general partial derivatives of matrix functions of the form f(A(x)) where A(x) is a matrix path of several variables (x=(x1,...,xj)). Building on results by Mathias [SIAM J. Matrix Anal. Appl., 17 (1996), pp. 610-620] for the first order derivative, we develop a block upper triangular form for higher order partial derivatives. This block form is used to derive conditions for existence and a generalized Daleckii-Krein formula for higher order derivatives. We show that certain specializations of this formula lead to classical formulas of quantum perturbation theory. We show how our results are related to earlier results for higher order Fréchet derivatives. Block forms of complex step approximations are introduced and we show how those are related to evaluation of derivatives through the upper triangular form. These relations are illustrated with numerical examples.

The ’black box’ characteristics of Convolutional Neural Networks (CNNs) present significant risks to their application scenarios, such as reliability, security, and division of responsibilities. Addressing the interpretability of CNN emerges as an urgent and critical issue in the field of machine learning. Recent research on CNN interpretability has either yielded unstable or inconsistent interpretations, or produced coarse-scale interpretable heatmaps, limiting their applicability in various scenarios. In this work, we propose a novel method of CNNs interpretation by incorporating a joint evaluation of multiple feature maps and employing multi-objective optimization (JE&MOO-CAM). Firstly, a method of joint evaluation for all feature maps is proposed to preserve the complete object instances and improve the overall activation values. Secondly, an interpretation method of CNNs under the MOO framework is proposed to avoid the instability and inconsistency of interpretation. Finally, the operators of selection, crossover, and mutation, along with the method of population initialization in NSGA-II, are redesigned to properly express the characteristics of CNNs. The experimental results, including both qualitative and quantitative assessments along with a sanity check conducted on three classic CNN models—VGG16, AlexNet, and ResNet50—demonstrate the superior performance of the proposed JE&MOO-CAM model. This model not only accurately pinpoints the instances within the image requiring explanation but also preserves the integrity of these instances to the greatest extent possible. These capabilities signify that JE&MOO-CAM surpasses six other leading state-of-the-art methods across four established evaluation criteria.

Large-scale electric vehicle (EV) charging scheduling is highly relevant for the growing number of EVs, while it can be complex to solve. A few existing studies have applied a two-stage scheduling approach to reduce computation time. The first stage approximates the optimal overall load, and the second prioritizes the charging. This work also attempts to apply such an approach for large-scale EV charging considering on-site photovoltaic (PV) generation at a workplace. However, validation and analysis are missing to address whether and why the two-stage approach is suitable. Besides, the existing studies lack exploring different methods to prioritize charging. This work investigates the two-stage approach. Simulation results show the non-uniqueness of the optimal solution from the optimal individual model, and guided by the optimal overall load, sorting-based methods can often lead to an optimal solution, while non-optimal solutions only cause decreases in the load-matching performance with a median value of less than 1%. The aggregated model usually cannot achieve the optimal overall load due to model simplifications. However, further applying sorting-based methods will reduce the differences between the final and the optimal overall load. Thus, the two-stage approach is suitable for this study, and further simulations show that it can achieve almost the optimal annual performance with around 1/57 of the computation time. Furthermore, this study explores different methods to prioritize charging. Simulation results show no difference in performance, while the Least Laxity First method leads to around 54.6% more switching., Flexergy KKS

Multicellular organisms, such as plants and animals, have independently evolved several times over the last hundreds of millions of years. The evolution of multicellularity has significantly shaped modern ecosystems, yet its origins remain largely unknown. Due to the ancient history and the small size scale of early multicellular organisms, few intact fossils have been preserved. To uncover the origins of large and complex life, researchers have turned to alternative methods such as phylogenetic modeling, experimental evolution, and theoretical frameworks. While these approaches have provided novel insights in the early steps of multicellular evolution, few studies have considered the role of adaptation in these novel life cycles. This thesis addresses the gap in our knowledge by employing mathematical modeling and computer simulations to study adaptation in novel multicellular life cycles. The first paper investigates the effects of unicellular reproduction modes, such as budding or binary fission, on the spread of growth rate mutations. It demonstrates that unicellular history significantly influences the adaptation rate, with budding cells exhibiting greater sensitivity to the spatial distribution of mutations. In Paper II, the role of multicellular reproduction mode for the adaptation of altruistic and selfish mutations is explored. Specifically, the study examines how adaptation is affected when the filaments are exposed to a size-based selective pressure. It reveals that while the adaptation of altruistic mutations is favored by large offspring, the spread of selfish mutations depends on both offspring size and selection strength. While Papers I and II assume deterministic life cycle structures at the multicellular level, paper III investigates the evolution of life cycle regulation when cells use internal information. The model demonstrates that when cells only have access to a limited amount of information, there is significant variation in the types of life

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/“on top” of it. Here the overlapping mesh is prescribed by a simple continuous motion, meaning that its location as a function of time is continuous and piecewise linear. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche’s method and also includes an integral term over the space-time boundary between the two meshes that mimics the standard discontinuous Galerkin time-jump term. The simple continuous mesh motion results in a space-time discretization for which standard analysis methodologies either fail or are unsuitable. We therefore employ what seems to be a relatively uncommon energy analysis framework for finite element methods for parabolic problems that is general and robust enough to be applicable to the current setting. The energy analysis consists of a stability estimate that is slightly stronger than the standard basic one and an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/“on top” of it. Here the overlapping mesh is prescribed by a simple discontinuous evolution, meaning that its location, size, and shape as functions of time are discontinuous and piecewise constant. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche’s method. The simple discontinuous mesh evolution results in a space-time discretization with a slabwise product structure between space and time which allows for existing analysis methodologies to be applied with only minor modifications. We follow the analysis methodology presented by Eriksson and Johnson (SIAM J Numer Anal 28(1):43–77, 1991; SIAM J Numer Anal 32(3):706–740, 1995). The greatest modification is the introduction of a Ritz-like “shift operator” that is used to obtain the discrete strong stability needed for the error analysis. The shift operator generalizes the original analysis to some methods for which the discrete subspace at one time does not lie in the space of the stiffness form at the subsequent time. The error analysis consists of an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

Cerebrovascular resistance (CVR) regulates blood flow in the brain, but little is known about the vascular resistances of the individual cerebral territories. We present a method to calculate these resistances and investigate how CVR varies in the hemodynamically disturbed brain. We included 48 patients with stroke/TIA (29 with symptomatic carotid stenosis). By combining flow rate (4D flow MRI) and structural computed tomography angiography (CTA) data with computational fluid dynamics (CFD) we computed the perfusion pressures out from the circle of Willis, with which CVR of the MCA, ACA, and PCA territories was estimated. 56 controls were included for comparison of total CVR (tCVR). CVR were 33.8 ± 10.5, 59.0 ± 30.6, and 77.8 ± 21.3 mmHg s/ml for the MCA, ACA, and PCA territories. We found no differences in tCVR between patients, 9.3 ± 1.9 mmHg s/ml, and controls, 9.3 ± 2.0 mmHg s/ml (p = 0.88), nor in territorial CVR in the carotid stenosis patients between ipsilateral and contralateral hemispheres. Territorial resistance associated inversely to territorial brain volume (p < 0.001). These resistances may work as reference values when modelling blood flow in the circle of Willis, and the method can be used when there is need for subject-specific analysis.