Dynamic layout optimization of truss subjected to a time-dependent load by isogeometric-analysis-based stiffness spreading method

A new kinetics calculation method using factorization and proper orthogonal decomposition (POD) is proposed. In the present method, discretized neutron balance equations that have fine and coarse time resolutions are derived using the factorization of the neutron flux. Then dimensionality reduction using POD is applied to the fine time-step calculation. The orthogonal basis for POD is constructed from the flux distributions at the current and previous coarse time steps on the fly. The fine time dependence captured in the fine time-step POD calculation is reflected in the coarse time-step calculation to accurately span the solution space around the next time step. The accuracy and performance of the present method are verified in the TWIGL benchmark problem. The calculation results show that the present method achieved a 26% speedup while maintaining accuracy compared to the conventional multigrid amplitude function method in the present calculation conditions.

Abstract The time-dependent Schrödinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials science. However, solving the TDSE for complex fermionic systems remains a significant challenge, particularly due to the need to capture the time-evolving many-body correlations, while the antisymmetric nature of fermionic wavefunctions complicates the function space in which these solutions must be represented. We propose a general-purpose neural network framework for solving the real-space TDSE, Fermionic Antisymmetric Spatio-Temporal Network, which treats time as an explicit input alongside spatial coordinates, enabling a unified spatiotemporal representation of complex, antisymmetric wavefunctions for fermionic systems. This approach formulates the TDSE as a global optimization problem, avoiding step-by-step propagation and supporting highly parallelizable training. The method is demonstrated on five benchmark problems: a 1D harmonic oscillator, interacting fermions in a time-dependent harmonic trap, 3D hydrogen orbital dynamics, a laser-driven hydrogen atom, and a laser-driven H$_2$ molecule, achieving excellent agreement with reference solutions across all cases. These results demonstrate the method's accuracy and flexibility within the bound-state manifold across various dimensions and interaction regimes. While the current localized Ansatz inherently restricts the description of extensive ionization and continuum states, the method demonstrates the capability to stably simulate coherent multi-electron dynamics over extended time windows. Our framework offers a highly expressive alternative to traditional basis-dependent or mean-field methods, opening new possibilities for ab initio simulations of time-dependent quantum systems, with applications in quantum dynamics, molecular control, and ultrafast spectroscopy.

Accurately integrating stiff ordinary differential equations (ODEs) and index-1 differential-algebraic equations that govern constrained multibody systems remains computationally demanding, especially for real-time applications. This article proposes an improved parsimonious physics-informed random-projection neural-network (PIRPNN) integrator that embeds explicit velocity- and position-correction into a single-hidden-layer random-feature framework and employs a vectorized assembly of system matrices for computation efficiency. Two illustrative examples are utilized to demonstrate the proposed algorithm and advantages. For the multibody dynamics benchmark problems examined, the improved PIRPNN demonstrates improved accuracy in terms of L 2 -trajectory error and energy drift, together with a notable reduction in computational cost compared with the original PIRPNN. At peculiar tolerances from 10 −6 to 10 −10 , it also outperforms the implicit MATLAB solvers ode15s and ode23t, further lowering both trajectory error and total-energy drift. The results underscore the potential of random-projection neural integrators as lightweight, constraint-preserving integration method alternative to classical integrators or more complex learning-based approaches in real-time multibody simulation.

A physics-informed machine learning framework based on holomorphic neural networks is introduced for detecting cracks in two-dimensional solids from strain or displacement data. Crack detection is formulated as an inverse problem in which the crack size, orientation, and location are treated as unknowns. The problem is solved using genetic optimization, where the fitness function is evaluated by expressing the solution of the corresponding plane elasticity problem in terms of holomorphic potentials, which are then determined through the training of two holomorphic neural networks. As the potentials satisfy equilibrium and traction-free conditions along the crack faces a priori, the training proceeds quickly based solely on boundary information. Training efficiency is further improved by splitting the genetic search into long-range and short-range stages, enabling the use of transfer learning in the latter. The new strategy is tested on three benchmark problems, showing that an optimal number of training epochs exists that provides the best overall performance. A comparison is also made with a popular crack detection approach that uses XFEM to compute the model response. Under the assumption of identical stress-field representation accuracy, the proposed method is found to be between 7 and 23 times faster than the XFEM-based approach. Furthermore, the proposed method appears to be less sensitive to noise in the input data. Overall, the present findings demonstrate that combining genetic optimization with holomorphic neural networks and transfer learning offers a promising avenue for developing crack detection strategies with higher efficiency than those currently available. • Crack detection formulated as an inverse problem and solved via genetic optimization. • Fitness evaluated by expressing the elastic solution in terms of complex potentials. • Complex potentials are determined by training two holomorphic neural networks. • Long-range and short-range searches are decoupled to leverage transfer learning. • Approach is 1 order of magnitude faster than common XFEM-based crack detection method.

• Comparative analysis of Finite Difference, Finite Volume, and Spectral Elements methods for full 3D time-domain acoustic wave propagation modelling. • Benchmarks ranging from simplified geometries that enable analytical comparison, to complex heterogeneous domains. • Implementation of a dedicated Finite volume-based acoustic solver in OpenFOAM with absorbing boundaries. • Comparison of omnidirectional and directional sources to analyze directivity effects on the resulting acoustic wave filed. • Best applicability range of each numerical method for near- and far- field acoustic prediction. A comparative study of three numerical methods - Finite Difference (FD), Finite Volume (FV), and Spectral Element Method (SEM) - for modeling underwater acoustic propagation is presented. The time-domain acoustic wave equation is solved using an in-house FD code, the open-source SPECFEM3D software for SEM, and a newly developed FV-based acoustic solver implemented and released within the OpenFOAM framework, extending a software environment traditionally used for computational fluid dynamics to underwater acoustics applications. The methods are systematically assessed through benchmark problems, ranging from homogeneous unbounded and semi-infinite domains to the Pekeris waveguide and a Gaussian canyon. Comparisons with analytical solutions demonstrate that all solvers accurately reproduce monopole and dipole radiation in simplified configurations. However, the analysis reveals that directional sources introduce non-trivial numerical sensitivities, even in simple environments. These effects manifest as spurious reflections and dispersion-related distortions, whose severity depends on the source implementation and the numerical scheme. The results show that SPECFEM3D generally provides the highest accuracy and robustness in heterogeneous and geometrically complex environments, while the in-house FD code and FV-based solver are more sensitive to dispersion but can recover accuracy through increased spatial resolution. Strategies to mitigate source-related artifacts, such as non-reflective hard sources and reduced source regions, are discussed. A preliminary investigation of moving sources highlights their straightforward implementation in FD and FV solvers, while requiring additional care within the SPECFEM3D framework. Overall, this work provides practical guidance on the accuracy, robustness, and applicability of different solvers for simulating underwater noise in near- and far-field conditions, while laying the ground for future source–propagation coupling within acoustic analogy frameworks in OpenFOAM.

The magneto-mechanical coupling governing the response of magnetorheological elastomers (MREs) requires computational tools for their design and optimization. The existing frameworks are customarily based on ideal boundary value problems that optimize MREs under ideal, non-realistic homogeneous magnetic sources. We present an approach that addresses these limitations by solving strongly coupled magneto-mechanical partial differential equations within the optimization loop, explicitly accounting for external permanent magnets and their interaction with the deformable elastomer. The approach combines a coupled magneto-elastic boundary value problem with an auxiliary mesh-motion problem, which allows the free-space to deform consistently with the MRE geometry. The direction of the remanent magnetization in the MRE is represented by continuous design fields, updated through a gradient-based optimizer with adjoint sensitivities and filtering. A series of benchmark problems demonstrate the framework: robustness with respect to the initial guess; symmetry of the solution under reversed polarity; influence of magnet placement; transition between external-field and self-interaction dominated actuation; and adaptation to opposite objectives in a pull-push actuator. The results highlight how the explicit modeling of the free-space and the magnetic source leads to robust and physically consistent designs, providing a foundation for advanced MRE-based actuators.

Multi-particle neural operator transformer for solving partial differential equations.

In this paper, meshfree collocation with fast-moving least-squares reproducing kernel was implemented to write down and execute numerical solutions for some applications in elastostatics and elastodynamics. The spatial discretization using meshfree collocation method was carried out on the equilibrium differential equations of elastostatics and elastodynamics and the corresponding boundary conditions. The resulting discrete forms were solved for benchmark problems in the one- and two-dimensional cases. In each case, a convergence study was conducted to ascertain the utility and efficacy of the developed solutions. For elastodynamics, the time domain, however, was discretized using the Newmark beta time-integration scheme. The latter combination was implemented to solve suitable benchmark problems in the one-dimensional and two-dimensional cases. In each case, a stability study was conducted to demonstrate, again, the method’s efficacy in handling elastodynamic problems.

We introduce and explore the automation and adaptation of partial neighborhood local search. Unlike traditional approaches requiring extensive parameter tuning, we design our approach to operate with minimal prerequisites. Specifically, we extend the sampled walk and ID walk algorithms by using distance-based calculations over a sliding window to determine the number of neighbors to evaluate at each step. To validate their performance, we empirically evaluate these parameter-free methods on four challenging combinatorial optimization benchmark problem classes from the literature, comparing them against fixed-parameter versions across multiple values. Our experiments show that, despite their simplicity, generic nature, and absence of parameters, these approaches achieve robust and competitive results across diverse problems-including different solution representations, neighborhood structures, and fitness landscape characteristics-thus validating the viability of generic autonomous local search methods.

Abstract Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as mixture models (MM) with an unknown number of components or the inference of overlapping signals in noisy data, as in the laser interferometer space antenna (LISA) global fit problem. Traditional approaches, such as product-space methods or reversible-jump Markov chain Monte Carlo (RJMCMC), often face efficiency and convergence limitations. This paper presents , a continuous-time Markov chain Monte Carlo (CTMCMC) framework that models parameter evolution through Poisson-driven birth, death, and mutation processes. is designed to sample models of unknown dimensionality. By requiring detailed balance through adaptive rate definitions, CTMCMC achieves automatic acceptance of trans-dimensional moves and high sampling efficiency. The code features waiting time weighted estimators, optimized memory storage, and a modular design for easy customization. We validate on three benchmark problems: an analytic trans-dimensional distribution, joint inference of sine waves and Lorentzians in time series, and a Gaussian MM with an unknown number of components. In all cases, the code shows excellent agreement with analytical and nested sampling results. All these features push as a powerful alternative to RJMCMC for large- and variable-dimensional Bayesian inference problems.

In this paper, a new high-order scheme is developed for solving the one-dimensional time-dependent convection-diffusion equation. In this new scheme, we expand the pseudo-source terms into k’th order Legendre polynomials. The expansion coefficients are obtained using the continuity condition of the current and the expressions of the centered-averaged values. To demonstrate the accuracy of the present scheme, four benchmark problems with known analytical solutions are solved. The results show that the proposed scheme provides highly accurate solutions, outperforming those obtained by the modified nodal integral method.

Solving constrained multiobjective optimization problems (CMOPs) is highly challenging due to the presence of complicated feasible regions, intense conflicts among objectives, and unevenly distributed constraints. As a result, conventional methods relying on a single constraint-handling mechanism frequently fail to maintain a stable equilibrium among solution feasibility, diversity, and convergence. To overcome these bottlenecks, this article introduces AFFCMO, a novel adaptive feasibility-guided framework tailored for constrained multiobjective optimization. At its core, the proposed approach utilizes a coevolutionary dual-population architecture that divides the search process into two distinct tasks. Specifically, an auxiliary population is tasked with global exploration, while a primary population focuses on the intensive exploitation of discovered feasible areas. To achieve this, the primary population leverages a DE/current-to-pbest/1 differential evolution strategy to closely approximate the constrained Pareto front. Simultaneously, the auxiliary population expands the search space using a mutation operator that adapts to the current evolutionary stage. Furthermore, exploration is bolstered by a multicriterion environmental selection scheme designed for the auxiliary group. By combining Euclidean geometric distributions, constraint relaxation, and value modeling inspired by epidemic dynamics, this strategy successfully preserves valuable infeasible solutions that can guide the search. Additionally, a dynamic resource allocation strategy based on historical search feedback and Thompson sampling is incorporated. This mechanism continuously evaluates the recent search contributions of both populations and adaptively adjusts their offspring sizes, thereby reducing the bias introduced by static allocation schemes. This mechanism continuously assesses the actual search contributions of both populations, allowing for the adaptive resizing of offspring generations and thereby eliminating the inherent biases of static allocation methods. Comprehensive empirical evaluations are conducted on 47 benchmark problems from four distinct test suites. The results indicate that AFFCMO significantly outperforms seven contemporary multiobjective evolutionary algorithms in terms of exploring complex feasible regions, preserving solution diversity, and achieving high convergence accuracy.

ABSTRACT We present a strongly coupled displacement () and pore water pressure () version of the Biot–Zienkiewicz (– ) equations in saturated porous media for the meshfree Lagrangian smoothed particle hydrodynamics (SPH) method. We propose two distinct formulations using a single particle layer, two‐phase framework, one based on a one‐step solution of a pressure Poisson equation (PPE formulation) and another allowing compressibility of the fluid resulting in an explicit rate equation for the pore pressure (PR formulation). We discuss both formulations from a numerical perspective and verify them using benchmark problems from poroelasticity, including Cryer's problem, as well as using undrained triaxial tests, where we additionally compare the results against a weakly coupled penalty‐based undrained framework for SPH. Beyond the formulations, the focus of this work is on modeling retrogressive landslides in saturated sensitive clays, which are particularly destructive due to their extended runout and fast movement. Our simulations emphasize performing strongly coupled hydromechanical modeling even for quasi‐undrained conditions, contrary to the predominant practices in the literature, as the structural features of the landslides change significantly when pore pressure dissipation and coupled effects are included. Additionally, spreads develop under a greater variety of slope conditions as opposed to the more fluidized flowslide type of retrogressive landslides captured when solely considering undrained behavior. Lastly, we apply the PR formulation to explore how slope steepness and height influence deformation modes and apply the framework to simulate the 1994 Sainte‐Monique landslide, recreating the topographic profile, runout, and deformation features post‐failure.

ABSTRACT The derivation of linearized equations and subsequent eigenvalue analysis is the basis for tasks such as frequency‐domain response analysis, control design, and stability assessment for mechanical systems. However, for general multibody systems with redundant or nonholonomic constraints, practical challenges persist in achieving numerically stable linearization and reliable eigenvalue analysis. This study provides numerically reliable linearization and eigenvalue analysis algorithms of Lagrange's equations of the first kind for general multibody systems, and forms a systematic computational framework. First, a robust linearization methodology is developed to automatically generate linearized state‐space equations. Coordinate partitioning is employed not only to eliminate redundant constraints and dependent coordinates, but also to significantly simplify the calculations. Second, a direct eigenvalue analysis on Redundant Coordinate Set Jacobians is performed instead of decomposing the state matrix, for its better numerical conditioning and sparsity. The equivalence of the eigenvalue problems is strictly proven theoretically. The methodology is validated by various benchmark problems and practical cases. The proposed approach has been implemented and released with a general‐purpose rigid‐flexible coupled multibody dynamics software INTESIM‐FMBD (v7.0), and provides a reliable numerical tool for linearizing general mechanical systems.

Abstract. This work presents SERGHEI-SWE-RE, a performance-portable, parallel model that couples a fully dynamic two-dimensional Shallow Water Equation (SWE) solver with a three-dimensional Richards Equation (RE) solver within the Kokkos framework to simulate surface–subsurface flow exchange. The model features a modular architecture with sequential coupling strategy, supporting both synchronous and asynchronous executions of surface and subsurface modules. The SERGHEI-SWE-RE model is validated against five benchmark problems incorporating stationary and fluctuating free-surface tests, a tilted v-catchment, a lateral-flow slope without ponding, and a heterogeneous superslab. The results demonstrate good agreement with established models. Asynchronous coupling reduces wall-clock time by up to about 75 % in the superslab case while preserving simulation accuracy. Strong and weak scaling tests on multiple Intel Xeon CPUs and NVIDIA GPUs reveal robust portability, with near-ideal RE scaling and less-satisfactory SWE scaling at high GPU counts, suggesting future improvements on differentiated meshes or more advanced domain decomposition strategies. Overall, the results presented establish SERGHEI-SWE-RE as an efficient, flexible and scalable model for integrated surface-subsurface flow simulations.

This paper describes the benchmark dataset for the electric vehicle routing problem with time windows. It is designed to facilitate the large-scale and reproducible evaluation of routing approaches under diverse charging scenarios. It is an extension of the Homberger 1000-customer vehicle-routing benchmark dataset through the incorporation of computationally derived charging-station data. For the 60 base instances included in the dataset, charging-station locations are randomly generated within the customer-coordinate bounds, and two variants are provided, resulting in 120 benchmark problems used in the validation and baseline analyses. A normalized local customer-density score is derived for each station. It is used to determine charging rates and log-normal parameters for prices and waiting times. Two variants are included in the dataset. Variant A maintains the original customer time-window constraints, while Variant B relaxes customer due dates based on the distance from the depot, subject to the depot closing time. The dataset is complemented by instance files, station attributes, parameters, and scripts. It also includes the results of feasibility tests, baseline solver tests, difficulty analyses, and sensitivity tests. These results show that the benchmark includes both easier and harder instance classes under different charging settings. Overall, the dataset is intended to support its use as a reproducible benchmark.

This paper presents two complementary classes of analytical benchmark problems for the one-dimensional wave equation governing longitudinal vibration of a prismatic rod with mixed (clamped–free) boundary conditions. The first benchmark class consists of classical initial-value problems and includes both compatible and incompatible initial data at the space–time corners, highlighting their influence on convergence, regularity, and termwise differentiation of displacement, velocity, and axial force series representations. The second benchmark class prescribes the displacement at two time instants (initial and final time), leading to a fundamentally different modal structure and revealing spectral conditioning effects governed by the ratio L/(cte). The derived closed-form solutions provide reference configurations for verification of transient numerical solvers, particularly in scenarios where classical smooth compatibility assumptions are not satisfied.

Quasi-Newton methods are among the most widely used and effective general-purpose algorithms for unconstrained optimization. These methods traditionally rely on the quasi-Newton equation, which serves as the foundation for updating approximations of the Hessian matrix at each iteration. The goal is to construct accurate second-order curvature information to accelerate convergence toward the optimum. In this paper, we derive a novel quasi-Newton equation based on an enhanced quadratic model. A key feature of this new formulation is that it incorporates both gradient information and objective function values, enabling higher-order accuracy in approximating the second-order curvature of the objective function. This new equation stands out for its ability to provide a more precise representation of the function's curvature, which in turn improves the overall efficiency and performance of the optimization method. Theoretical analysis shows that the proposed method is globally convergent under certain reasonable assumptions. To validate the effectiveness of the approach, we conducted a series of numerical experiments using standard benchmark problems. The results demonstrate that the modified Broyden, Fletcher, Goldfarb, and Shanno (BFGS) method, which integrates the new quasi-Newton equation, outperforms existing BFGS-type methods in terms of numerical efficiency and solution accuracy.

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The POMDP framework allows for modeling and solving sequential decision-making problems under observation uncertainty. In complex, high-dimensional, partially observable environments, existing methods for inference based on exact computations (e.g., via Bayes' theorem) or sampling algorithms do not always scale well. Furthermore, ground truth states may not be available for learning the exact transition dynamics. DBMMs extend deep Markov models into the partially observable decision-making framework and allow efficient belief inference entirely based on available observation data via variational inference methods. By leveraging the potency of neural networks, DBMMs can infer and simulate non-linear relationships in the system dynamics and naturally scale to problems with high dimensionality and discrete or continuous variables. In addition, neural network parameters can be dynamically updated efficiently based on data availability. DBMMs can thus be used to infer a belief variable, thus enabling the derivation of POMDP solutions over the belief space. We evaluate the efficacy of the proposed methodology by evaluating the capability of model-formulation agnostic inference of DBMMs in benchmark problems that include discrete and continuous variables. Finally, we demonstrate the practical utility of the inferred beliefs in a downstream decision-making task, showing that an RL agent guided by DBMMs beliefs significantly outperforms powerful model-free baselines and achieves near-optimal performance.1.