This paper proposes an extended r-adaptive isogeometric analysis framework for problems exhibiting weak discontinuities in solution derivatives, where discretization errors are often dominated by insufficient resolution of material interfaces. The method combines enrichment functions with a control-point relocation strategy guided by a Gaussian monitor constructed from an aggregated level-set representation of the interfaces. Rather than refining the mesh, resolution is redistributed according to interface geometry, enabling sharp representation of gradient jumps while preserving exact CAD geometry, spline topology, and a fixed number of degrees of freedom. Benchmark examples indicate up to 65.7% error reduction relative to enrichment-only formulations, and even larger improvements compared with standard IGA, while introducing less than 1% additional computational cost. The results demonstrate that redistributing geometric resolution provides an efficient alternative to conventional refinement-based adaptive strategies for weak-discontinuous problems.

This study introduces a framework for learning a low-depth surrogate quantum circuit (SQC) that approximates the nonlinear, dissipative, and hence non-unitary Bhatnagar–Gross–Krook (BGK) collision operator in the lattice Boltzmann method (LBM) for the (Formula presented.) lattice. By appropriately selecting the quantum state encoding, circuit architecture, and measurement protocol, non-unitary dynamics emerge naturally within the physical population space. This approach removes the need for probabilistic algorithms relying on ancilla qubits and post-selection to reproduce dissipation, or for multiple state copies to capture nonlinearity. The SQC is designed to preserve key physical properties of the BGK operator, including mass conservation, scale equivariance, and (Formula presented.) equivariance, while momentum conservation is encouraged through penalization in the training loss. When compiled to the IBM Heron quantum processor's native gate set, assuming all-to-all qubit connectivity, the circuit requires only 724 native gates and operates locally on the velocity register, making it independent of the lattice size. The learned SQC is validated on two benchmark cases, the Taylor–Green vortex decay and the lid-driven cavity, showing accurate reproduction of vortex decay and flow recirculation. While integration of the SQC into a quantum LBM framework presently requires measurement and re-initialization at each timestep, the necessary steps towards a measurement-free formulation are outlined.

Fast numerical predictions have become an indispensable component of modern engineering design workflows, whether in interactive design within computer-aided design (CAD) environments or in multi-query numerical tasks such as design optimization and uncertainty quantification. Depending on the context, “fast” may refer to near real-time predictions within a few seconds, or simply to methods that are significantly faster than high-fidelity simulations, for example those based on the finite element method (FEM). With the aim of providing a tool that not only enables such accelerated predictions but also integrates seamlessly into established workflows, we introduce the concept of IGANets. IGANets are spline-based, physics-informed machine learning models that can be integrated naturally between CAD representations and numerical analysis tools, particularly those based on isogeometric analysis (IGA). Unlike purely data-driven approaches, IGANets do not inherently rely on precomputed training data; instead, they are formulated in a collocation setting directly from physical models. In this paper, we present the IGANets concept and demonstrate its feasibility through numerical experiments for the Poisson equation and linear elasticity. In addition, we investigate a multi-instance linear-elasticity setting with varying I-beam-like geometries and boundary conditions in order to assess the generalization capability of the framework. The results show that IGANets can predict solutions for previously unseen problem instances within the training range with improved accuracy as the number of training samples increases.

Lattice Gas Automata (LGA) is a classical method for simulating physical phenomena, including Computational Fluid Dynamics (CFD). Quantum LGA (QLGA) is the family of methods that implement LGA schemes on quantum computers. In recent years, QLGA has garnered attention from researchers thanks to its potential of efficiently modeling CFD processes by either reducing memory requirements or providing simultaneous representations of exponentially many LGA states. In this work, we introduce novel building blocks for QLGA algorithms that rely on computational basis state encodings. We address every step of the algorithm, from initial conditions to measurement, and provide detailed complexity analyses that account for all discretization choices of the system under simulation. We introduce multiple ways of instantiating initial conditions, efficient boundary condition implementations for novel geometrical patterns, a novel collision operator that models less restricted interactions than previous implementations, and quantum circuits that extract quantities of interest out of the quantum state. For each building block, we provide intuitive examples and open-source implementations of the underlying quantum circuits.

Modeling open-hole failure of composites is a complex task, consisting of a highly nonlinear response with interacting failure modes. Numerical modeling of this phenomenon has traditionally been based on the finite element method, but requires to tradeoff between high fidelity and computational cost. To mitigate this shortcoming, recent work has leveraged machine learning to predict the strength of open-hole composite specimens. Here, we also propose using data-based models to tackle open-hole composite failure from a classification point of view. More specifically, we show how to train surrogate models to learn the ultimate failure envelope of an open-hole composite plate under in-plane loading. To achieve this, we solve the classification problem via support vector machine (SVM) and test different classifiers by changing the SVM kernel function. The flexibility of kernel-based SVM also allows us to integrate the recently developed quantum kernels in our algorithm and compare them with the standard radial basis function kernel. Finally, thanks to kernel-target alignment optimization, we tune the free parameters of all kernels to best separate safe and failure-inducing loading states. The results show classification accuracies higher than 90% for RBF, especially after alignment, followed closely by the quantum kernel classifiers.

Thermal modeling of Laser Powder Bed Fusion (LPBF) is challenging due to steep, rapidly moving thermal gradients induced by the laser, which are difficult to resolve accurately with conventional Finite Element Methods (FEM). Highly refined, dynamically adaptive spatial discretization is typically required, leading to prohibitive computational costs. Semi-analytical approaches mitigate this by decomposing the temperature field into an analytical point-source solution and a complementary numerical field that enforces boundary conditions. However, state-of-the-art implementations either necessitate extensive mesh refinement near boundaries or rely on restrictive image-source techniques, limiting their efficiency and applicability to complex geometries. This study presents a novel reformulation of the semi-analytical framework using Isogeometric Analysis (IGA). The laser heat input is captured by the analytical point-source solution, while the complementary correction field, which imposes boundary conditions, is solved using a spline-based IGA discretization. The governing heat equation for the correction field is cast in a weak form, discretized with NURBS basis functions, and advanced in time using an implicit θ-scheme. This approach leverages IGA’s key advantages: exact geometry representation, higher-order continuity, and superior accuracy per degree of freedom. These features unlock efficient thermal modeling of realistic parts with complex contours. Our strategy eliminates the need for scan-wise remeshing and robustly handles intricate geometric features like sharp corners and varying cross-sections. Numerical examples demonstrate that the proposed semi-analytical IGA method delivers accurate temperature predictions and achieves substantial computational efficiency gains compared to standard FEM, establishing it as a powerful new tool for high-fidelity thermal simulation in LPBF.

This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when applied to IGA solvers, including geometric accuracy issues, interpolation errors, and substantial communication overhead. The methodology draws on the IGA mathematical framework to deliver coupling solutions that preserve the high-order continuity and exact geometric representation of splines. We develop two complementary strategies: (1) a spline-vertex coupling method that enables efficient interaction between IGA and conventional solvers, and (2) a fully isogeometric coupling approach that maximizes accuracy for IGA-to-IGA communication. Both theoretical analysis and extensive numerical experiments demonstrate that our spline-based methods significantly reduce communication overhead compared to traditional approaches while simultaneously enhancing geometric accuracy through exact boundary representation and maintaining higher-order solution continuity across the coupled interfaces. We quantitatively confirm the communication efficiency benefits through systematic measurements of both transfer times and data volumes across various mesh refinement levels, with experimental results closely aligning with our theoretical predictions. Our benchmark studies further demonstrate the geometric fidelity advantages through exact boundary representation, while also highlighting how the inherent mathematical structure of splines naturally preserves solution derivatives across interfaces without requiring additional computation or specialized transfer algorithms. This work not only provides efficient coupling strategies tailored to IGA-based solvers but also establishes a practical bridge between IGA and traditional discretization methods in partitioned multiphysics simulations. By offering viable options for coupling conventional solvers with IGA-based components, our approach enables broader adoption of IGA in established simulation workflows while ensuring accurate and high-performance interface communications.

Benchmarking quantum computers helps to quantify them and bringing the technology to the market. Various application-level metrics exist to benchmark a quantum device at an application level. This paper presents a revised holistic scoring method called the Quantum Application Score (QuAS) incorporating strong points of previous metrics, such as QPack and the Q-score. We discuss how to integrate both and thereby obtain an application-level metric that better quantifies the practical utility of quantum computers. We evaluate the new metric on different hardware platforms such as D- Wave and IBM as well as quantum simulators of Quantum Inspire and Rigetti.

Part-scale thermal process simulations play an important role in improving the part quality of the Laser Powder Bed Fusion (LPBF) process. The semi-analytical simulation method relies on the superposition of analytical fields to represent laser-induced heat sources in a semi-infinite space and a complementary temperature field to enforce boundary conditions. So far, boundary conditions have been imposed by analytical image fields for straight boundaries and numerically for non-straight boundaries. The latter requires considerable refinement on the spatial discretization, at least near the boundaries, and compromises the computational efficiency of the simulations. In this paper, we derive a closed-form solution for the image fields that can accurately enforce the boundary conditions for non-straight boundaries. A geometrically complex part boundary is represented by B-splines, and with the aid of an offset method and reparameterization, the positions of the image sources are determined. The image field's closed-form expression is then found using the boundary's local curvature calculated from the local tangent lines. Numerical examples on different levels of complexity revealed that the net heat lost along an adiabatic boundary vanishes when the novel image source solutions are used, and the thermal evolution of complex parts can be accurately predicted with high computational efficiency. Simulations involving multiple lasers can also be performed with no extra computational cost.

We present QLBM, a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). QLBM is a modular framework that introduces a quantum component abstraction hierarchy tailored to the implementation of novel QBMs. The framework interfaces with state-of-the-art quantum software infrastructure to enable efficient simulation and validation pipelines, and leverages novel execution and pre-processing techniques that significantly reduce the computational resources required to develop quantum circuits. We demonstrate the versatility of the software by showcasing multiple QBMs in 2D and 3D with complex boundary conditions, integrated within automated benchmarking utilities. Accompanying the source code are extensive test suites, thorough online documentation resources, analysis tools, visualization methods, and demos that aim to increase the accessibility of QBMs while encouraging reproducibility and collaboration. Program summary: Program Title: QLBM CPC Library link to program files: https://doi.org/10.17632/28hkvsg7p2.1 Developer's repository link: https://github.com/QCFD-Lab/qlbm Licensing provisions: MPL-2.0 Programming language: Python3 Supplementary material: The documentation of is available at https://qcfd-lab.github.io/qlbm/. Nature of problem: The advent of quantum algorithms for computational fluid dynamics brings with it challenges that are new to the established field of computational physics. These challenges include the lack of standardized implementations of the still nascent quantum methods, the intense computational demands of developing and simulating quantum algorithms on hardware available today, and the absence of tools that integrate novel developments into established infrastructure. Because of these current limitations, physicists and mathematicians expend superfluous resources on tasks that more mature computational physics branches have surmounted long ago. Solution method: QLBM is a software package that provides an end-to-end development environment for quantum lattice Boltzmann methods. The modular design and flexible quantum circuit library provide a base for extending and generalizing quantum algorithms. Performance enhancements exploit the paradigm of quantum computing simulations to accelerate the speed at which researchers can verify the validity of their methods. Its integration with state-of-the-art quantum computing software and visualization tools increases the algorithms' accessibility. These features allow QLBM to effectively generate, simulate, and analyze quantum circuits for 2D and 3D computational fluid dynamics problems.

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness. Numerical modelling typically involves thin shell formulations. As the mesh resolution depends on the wrinkle wave lengths, the analysis can become computationally expensive for shorter ones. Implicitly modelling the wrinkles using a modified kinematic or constitutive relationship based on a taut, slack or wrinkled state derived from a so-called tension field, a simplification is introduced in order to reduce computational efforts. However, this model was restricted to linear elastic material models in previous works. Aiming to develop an implicit isogeometric wrinkling model for large strain and hyperelastic material applications, a modified deformation gradient has been assumed, which can be used for any strain energy density formulation. The model is an extension of a previously published model for linear elastic material behaviour and is generalised to other types of discretisation as well. The extension for hyperelastic materials requires the derivative of the material tensor, which can be computed numerically or derived analytically. The presented model relies on a combination of dynamic relaxation and a Newton–Raphson solver, because of divergence in early Newton–Raphson iterations as a result of a changing tension field, which is not included in the stress tensor variation. Using four benchmarks, the model performance is evaluated. Convergence with the expected order for Newton–Raphson iterations has been observed, provided a fixed tension field. The model accurately approximates the mean surface of a wrinkled membrane with a reduced number of degrees of freedom in comparison to a shell solution.

In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path toward solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and fault-tolerant many-qubit systems become available. The major challenge in developing a start-to-end quantum algorithm for the Boltzmann equation consists in encoding relevant data efficiently in quantum bits (qubits) and formulating the streaming, collision and reflection steps as one comprehensive unitary operation. The current literature on quantum Boltzmann methods mostly proposes data encodings and quantum primitives for individual phases of the pipeline, assuming that they can be combined to a full algorithm. In this paper, we disprove this assumption by showing that for encodings commonly discussed in the literature, either the collision or the streaming step cannot be unitary. Building on this landmark result, we propose a novel encoding in which the number of qubits used to encode the velocity depends on the number of time steps one wishes to simulate, with the upper bound depending on the total number of grid points. In light of the non-unitarity result established for existing encodings, our encoding method is to the best of our knowledge the only one currently known that can be used for a start-to-end quantum Boltzmann solver where both the collision and the streaming step are implemented as a unitary operation.

As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

Noisy intermediate-scale quantum computers (NISQ) are computing hardware in their childhood, but they are showing high promise and growing quickly. They are based on so-called qubits, which are the quantum equivalents of bits. Any given qubit state results in a given probability of observing a value of zero or one in the readout process. One of the main concerns for NISQ machines is the inherent noisiness of qubits, i.e., the observable frequencies of zeros and ones do not correspond to the theoretically expected probability, as the qubit states are subject to random disturbances over time and with each additional algorithmic operation applied to them. Models to describe the influence of this noise exist.In this study, we conduct extensive experiments on quantum noise. Based on our data, we show that existing noise models lack important aspects. Specifically, they fail to properly capture the aggregation of noise effects over time (or over an algorithm's runtime), and they are underdispersed. With underdispersion, we refer to the fact that observable frequencies scatter much more between repeated experiments than what the standard assumptions of the binomial distribution would allow for. Based on these shortcomings, we develop an extended noise model for the probability distribution of observable frequencies as a function of the number of gate operations. The model roots back to a known continuous random walk on the (Bloch) sphere, where the angular diffusion coefficient can be used to characterize the standard noisiness of gate operations. Here, we superimpose a second random walk at the scale of multiple readouts to account for overdispersion. Further, our model has known, explicit components for noise during state preparation and measurement. The interaction of these two random walks predicts theoretical, runtime-dependent bounds for probabilities. Overall, it is a three-parameter distributional model that fits the data much better than the corresponding one-scale model (without overdispersion), and we demonstrate the better fit and the plausibility of the predicted bounds via Bayesian data-model analysis.

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface parameters with respect to the produced irradiance distribution. To prevent the optimizer from getting trapped in local minima, we gradually increase the number of degrees of freedom of the surface by using Truncated Hierarchical B-splines (THB-splines) during optimization. The refinement locations are determined by analyzing the gradients of the surface vertices. We first design a freeform using a collimated beam (zero-etendue source) for a complex target distribution to demonstrate the method’s effectiveness. Then, we demonstrate the ability of this approach to create a freeform that can project the light of an extended Lambertian source into a prescribed target distribution.