arXiv subjects

M. H. Aliabadi

Publications and source records attributed to M. H. Aliabadi.

8 recordsLinked to original sources

arXiv2026

Exceptional-point conjugate symmetry and migration in fluid-loaded elastic waveguides: restructuring the physical dispersion spectrum

The dispersion spectrum of a fluid-loaded elastic waveguide is a non-Hermitian system with eigenmodes on a two-sheeted Riemann manifold. Although exceptional points (EPs) organize avoided crossings, the topological rules by which fluid loading restructures the observable spectrum (both physically admissible modes and their connectivity) remain unknown, and conventional solvers fail to recover complete branches. Here we establish these rules. We prove that, for real elastic moduli and real fluid parameters, EPs obey a conjugate-pair symmetry, and that a pair on the physical sheet enforces an avoided crossing of real wavenumbers between the two modes it controls, yielding a topological criterion for mode identification. We then identify two independent reconstruction mechanisms. First, the physical observation space expands continuously: a mode observable above its vacuum cut-off can extend downward to the sound line, admitting solutions in a frequency band empty in vacuum; vacuum-anchored seeds above cut-offs continued downward capture such branches systematically. Second, EP migration rewires mode connectivity: as fluid density increases, conjugate pairs leaving the physical sheet (signaled by a sign reversal of the imaginary part of either the in-plane or the vertical wavenumber) leave the two previously coupled physical branch segments unconnected by any EP within the observation space; they become independent curves that may intersect freely on the real frequency axis, with the narrowest veerings losing their topological protection first. Mirror-symmetry breaking births additional EPs generically in the trapped regime but only conditionally in the leaky regime. Numerical computations on symmetric and asymmetric composite laminates under single- and double-sided water loading validate the framework, recovering multiple leaky branches missed by standard solvers.

physics.comp-ph↗

arXiv2026

Steering topology distributions for unified generative design of architected metamaterials

Architected metamaterials derive their functions from structure, creating vast opportunities to program physical responses through topology design. However, existing design methods are often tailored to individual design problems, making limited use of topology knowledge for effective and broadly applicable design as objectives, constraints, and physical functions change. Here we introduce Generative Topology Optimization (GenTO), a unified framework that turns a learned topology prior into a reusable design engine. GenTO trains a diffusion model on a large full-order topology dataset and then iteratively steers the resulting topology distribution toward task-specific high-performing regions using user-defined physical objectives and constraints. This shifts the object of optimization from a single structure to a task-adapted topology distribution. Across topology design problems spanning thermal extremization, multi-objective morphology control, property-targeted auxetic design, and vibration transmission design, GenTO reuses pretrained topology priors for heterogeneous tasks, preserves structural diversity, and reaches high-performing solutions supported by numerical benchmarks and experimental validation. These results establish reusable topology knowledge as a unified principle for effective and scalable architected metamaterial design.

cs.AI↗

arXiv2026

Mode veering and symmetry-protected crossings in conservative elastic waveguides: unified perturbation-theoretic interpretation and adaptive tracking

Accurate mode tracking is essential for elastic waveguide dispersion analysis in ultrasonic nondestructive evaluation and structural health monitoring. Its reliability, however, deteriorates near mode veering and closely spaced eigenvalues, where rapid eigenvector exchange causes mode misidentification. Although widely observed, the quantitative relationship between veering, eigenvector evolution, and tracking robustness has not been systematically established. By specializing classical perturbation theory to the single-parametric Hermitian SAFE eigenproblem--exemplified by conservative elastic waveguides--we obtain explicit expressions for eigenvector derivatives and modal coupling strength. This yields a unified, quantitative interpretation of mode veering, symmetry-protected crossings, and degeneracies, and clarifies their distinct tracking implications: eigenvector sensitivity scales inversely with the eigengap, explaining modal repulsion and the degradation of correlation-based tracking near avoided crossings, whereas symmetry-protected crossings remain benign because symmetry-induced decoupling preserves smooth eigenvector evolution, and symmetry-protected degeneracies require rotation-invariant subspace tracking. A numerical consistency condition and an existence result for a critical step size are then derived, motivating a two-level adaptive strategy with an a posteriori error indicator that separates numerical tracking consistency from symmetry-based physical correctness. Numerical examples validate the theoretical predictions and demonstrate improved robustness in regions of strong modal interaction, providing practical guidance for reliable dispersion calculations and ultrasonic inspection.

math.NA↗

arXiv2026

Homotopy continuation of viscoelastic waveguide dispersion curves: from intra-manifold tracking to inter-manifold transport

Conventional mode tracking operates in the dark: it traces dispersion branches on the non-Hermitian eigenvalue manifold using only local continuity, unaware of the global Riemann-sheet topology. When exceptional points (EPs) lie close to the real frequency axis, the eigenvector similarity that local trackers rely on degrades, and mode tracking becomes unreliable, failing silently. This paper replaces blind intra-manifold tracking with inter-manifold transport. A material attenuation parameter s in [0,1] continuously maps the target lossy problem to an auxiliary lossless one whose Hermitian eigenvalue problem yields a well-posed anchor manifold on which each dispersion branch possesses a globally unique and continuous identity. These identities are defined once on the elastic anchor and then transported to the viscoelastic target via predictor-corrector homotopy continuation; as long as the path avoids all EPs, branch identity is preserved throughout the transport. For any mode pair whose EPs have not crossed the real frequency axis (Type I), the transported identities are inherited automatically. In contrast, when an EP crosses the real axis and becomes Type II, the topology differs from the elastic anchor and a label swap is required. The framework is validated on symmetric and unsymmetric laminates, with most cases at loss factors of 0.003 to 0.02; for all Type I pairs in these cases the identities are inherited without alteration. For a challenging unsymmetric laminate at 0.05, several EP pairs have become Type II, yet the homotopy transport still produces numerically accurate solutions. Two diagnostic signatures--an extremely sharp imaginary-part crossing and a marked discrepancy between spectral group velocity and energy flux velocity--identify where the underlying EP topology demands a label swap.

math.NA↗

arXiv2026

Discrete Solution Operator Learning for Geometry-Dependent PDEs

Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological changes, abrupt changes in boundary conditions or boundary types, and changes in the computational domain, which break the smooth-variation premise. Here we introduce Discrete Solution Operator Learning (DiSOL), a complementary paradigm that learns discrete solution procedures rather than continuous function-space operators. DiSOL factorizes the solver into learnable stages that mirror classical discretizations: local contribution encoding, multiscale assembly, and implicit solution reconstruction on an embedded grid, thereby preserving procedure-level consistency while adapting to geometry-dependent discrete structures. Across geometry-dependent Poisson, advection-diffusion, linear elasticity, as well as spatiotemporal heat conduction problems, DiSOL produces stable and accurate predictions under both in-distribution and strongly out-of-distribution geometries, including discontinuous boundaries and topological changes. These results highlight the need for procedural operator representations in geometry-dominated problems and position discrete solution operator learning as a distinct, complementary direction in scientific machine learning.

cs.LG↗

arXiv2025

Physics-guided impact localisation and force estimation in composite plates with uncertainty quantification

Physics-guided approaches offer a promising path toward accurate and generalisable impact identification in composite structures, especially when experimental data are sparse. This paper presents a hybrid framework for impact localisation and force estimation in composite plates, combining a data-driven implementation of First-Order Shear Deformation Theory (FSDT) with machine learning and uncertainty quantification. The structural configuration and material properties are inferred from dispersion relations, while boundary conditions are identified via modal characteristics to construct a low-fidelity but physically consistent FSDT model. This model enables physics-informed data augmentation for extrapolative localisation using supervised learning. Simultaneously, an adaptive regularisation scheme derived from the same model improves the robustness of impact force reconstruction. The framework also accounts for uncertainty by propagating localisation uncertainty through the force estimation process, producing probabilistic outputs. Validation on composite plate experiments confirms the framework's accuracy, robustness, and efficiency in reducing dependence on large training datasets. The proposed method offers a scalable and transferable solution for impact monitoring and structural health management in composite aerostructures.

physics.data-an↗

arXiv2025

Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics

PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems. These challenges become evident when comparing the limitations of PINN with the well-established numerical methods commonly used in solid mechanics, such as the finite element method (FEM). Specifically: a) PINN models generate solutions over an infinite domain, which conflicts with the finite boundaries typical of most solid structures; and b) the solution space utilised by PINN is Euclidean, which is inadequate for addressing the complex geometries often present in solid structures. This work presents a PINN architecture for general solid mechanics problems, referred to as the Finite-PINN model. The model is designed to effectively tackle two key challenges, while retaining as much of the original PINN framework as possible. To this end, the Finite-PINN incorporates finite geometric encoding into the neural network inputs, thereby transforming the solution space from a conventional Euclidean space into a hybrid Euclidean-topological space. The model is comprehensively trained using both strong-form and weak-form loss formulations, enabling its application to a wide range of forward and inverse problems in solid mechanics. For forward problems, the Finite-PINN model efficiently approximates solutions to solid mechanics problems when the geometric information of a given structure has been preprocessed. For inverse problems, it effectively reconstructs full-field solutions from very sparse observations by embedding both physical laws and geometric information within its architecture.

cs.CE↗

arXiv2025

Robust impact localisation on composite aerostructures using kernel design and Bayesian fusion under environmental and operational uncertainties

Impact localisation on composite aircraft structures remains a significant challenge due to operational and environmental uncertainties, such as variations in temperature, impact mass, and energy levels. This study proposes a novel Gaussian Process Regression framework that leverages the order invariance of time difference of arrival (TDOA) inputs to achieve probabilistic impact localisation under such uncertainties. A composite kernel function, combining radial basis function and cosine similarity kernels, is designed based on wave propagation dynamics to enhance adaptability to diverse conditions. Additionally, a task covariance kernel is introduced to enable multitask learning, facilitating the joint prediction of spatial coordinates while capturing interdependencies between outputs. To further improve robustness and accuracy, Bayesian model averaging is employed to dynamically fuse kernel predictions, assigning adaptive weights that account for varying conditions. Extensive experimental validation on a composite plate, including scenarios with large-mass drop tower impacts and small-mass guided drop mass impacts, demonstrates the proposed method's robustness and generalisability. Notably, the framework achieves accurate localisation without requiring compensation strategies for variations in temperature or impact mass, highlighting its suitability for real-world applications. The study also highlights the critical role of sample standardisation for preprocessing TDOA inputs, demonstrating its superiority over feature standardisation by preserving TDOA order invariance and enhancing model compatibility. These advancements establish the proposed method as a reliable and effective solution for structural health monitoring in complex and uncertain operational environments.

stat.AP↗