arXiv subjects

Navid Valizadeh

Publications and source records attributed to Navid Valizadeh.

9 recordsLinked to original sources

arXiv2026

Neural Operators for Immersed-Boundary Soft Swimmers Locomotion

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid--structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

cs.LG↗

arXiv2025

Phase-field modeling of multicomponent vesicles in viscoelastic fluid

Multicomponent vesicles suspended in viscoelastic fluids are crucial for understanding a variety of physiological processes. In this work, we develop a continuum surface force (CSF) phase-field model to investigate the hydrodynamics of inextensible multicomponent vesicles in viscoelastic fluid flows with inertial forces. Our model couples a fluid field comprising both Newtonian and Oldroyd-B fluids, a surface concentration field representing the multicomponent distribution on the vesicle membrane, and a phase-field variable governing the membrane evolution. The viscoelasticity effect of extra stress is well incorporated into the full Navier-Stokes equations in the fluid field. The surface concentration field is determined by Cahn-Hilliard equations, while the membrane evolution is governed by a nonlinear advection-diffusion equation. The membrane is coupled to the surrounding fluid through the continuum surface force (CSF) framework. To ensure stable numerical solutions of the highly nonlinear multi-field model, we employ a residual-based variational multiscale (RBVMS) method for the Navier-Stokes equations, a Streamline-Upwind Petrov-Galerkin (SUPG) method for the Oldroyd-B equations, and a standard Galerkin finite element framework for the remaining equations. The system of PDEs is solved using an implicit, monolithic scheme based on the generalized-$\alpha$ time integration method. To enhance spatial accuracy, we employ isogeometric analysis (IGA). We present a series of two-dimensional numerical examples in shear and Poiseuille flows to elucidate the influence of membrane composition and fluid viscoelasticity on the hydrodynamics of multicomponent vesicles.

physics.flu-dyn↗

arXiv2025

PENCO: A Physics-Energy-Numerics-Consistent Operator for 3D Phase Field Modeling

Accurate and efficient solutions of spatiotemporal partial differential equations (PDEs), such as phase-field models, are fundamental for understanding interfacial dynamics and microstructural evolution in materials science and fluid mechanics. Neural operators (NOs) have recently emerged as powerful data-driven alternatives to traditional solvers; however, existing architectures often accumulate temporal errors, struggle to generalize over long temporal horizons, and require large training datasets. To overcome these limitations, we propose PENCO (Physics-Energy-Numerics-Consistent Operator), a hybrid operator-learning framework that integrates physical laws with data-driven neural operator methods, using either the Fourier Neural Operator (FNO-4D) or the Multi-Head Neural Operator (MHNO) architecture as the backbone. The formulation introduces an enhanced L^2 Gauss-Lobatto collocation residual around the temporal midpoint that robustly enforces the governing dynamics and significantly improves accuracy, a Fourier-space numerical consistency term that captures the balanced behavior of semi-implicit discretizations, and an energy-dissipation constraint that ensures thermodynamic consistency. Additional low-frequency spectral anchoring and teacher-consistency mechanisms further stabilize learning and suppress long-term error growth. This hybrid design enables PENCO to preserve governing physics while mitigating long-term error growth. Through extensive three-dimensional phase-field benchmarks on periodic cubic domains, covering phase ordering, crystallization, epitaxial growth, and complex pattern formation, PENCO demonstrates superior accuracy, stability, and data efficiency compared to state-of-the-art neural operators, including FNO-4D and MHNO, while maintaining physically consistent evolution. The associated dataset and implementation are available at github.com/MBamdad/PENCO.

physics.comp-ph↗

arXiv2025

NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers

Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks. Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution. Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers by producing high-quality initial guesses for Krylov methods such as conjugate gradient and GMRES. NOWS leaves existing discretizations and solver infrastructures intact, integrating seamlessly with finite-difference, finite-element, isogeometric analysis, finite volume method, etc. Across our benchmarks, the learned initialization consistently reduces iteration counts and end-to-end runtime, resulting in a reduction of the computational time of up to 90 %, while preserving the stability and convergence guarantees of the underlying numerical algorithms. By combining the rapid inference of neural operators with the rigor of traditional solvers, NOWS provides a practical and trustworthy approach to accelerate high-fidelity PDE simulations.

cs.LG↗

arXiv2025

Multi-Head Neural Operator for Modelling Interfacial Dynamics

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential equations (PDEs). Traditional numerical methods, including finite difference, finite element, and spectral techniques, often become computationally prohibitive when dealing with high-dimensional problems or systems with multiple scales. Neural operators (NOs), a class of deep learning models, have emerged as a promising alternative by learning mappings between function spaces and efficiently approximating solution operators. In this work, we introduce the Multi-Head Neural Operator (MHNO), an extended neural operator framework specifically designed to address the temporal challenges associated with solving time-dependent PDEs. Unlike existing neural operators, which either struggle with error accumulation or require substantial computational resources for high-dimensional tensor representations, MHNO employs a novel architecture with time-step-specific projection operators and explicit temporal connections inspired by message-passing mechanisms. This design allows MHNO to predict all time steps after a single forward pass, while effectively capturing long-term dependencies and avoiding parameter overgrowth. We apply MHNO to solve various phase field equations, including antiphase boundary motion, spinodal decomposition, pattern formation, atomic scale modeling, and molecular beam epitaxy growth model, and compare its performance with existing NO-based methods. Our results show that MHNO achieves superior accuracy, scalability, and efficiency, demonstrating its potential as a next-generation computational tool for phase field modeling. The code and data supporting this work is publicly available at https://github.com/eshaghi-ms/MHNO.

physics.comp-ph↗

arXiv2024

Hierarchical multiscale fracture modeling of carbon-nitride nanosheet reinforced composites by combining cohesive phase-field and molecular dynamics

Understanding the fracture mechanisms in composite materials across scales, from nano- to micro-scales, is essential for an in-depth understanding of the reinforcement mechanisms and designing the next generation of lightweight, high-strength composites. However, conventional methods struggle to model the complex fracture behavior of nanocomposites, particularly at the fiber-matrix interface. The phase-field regularized cohesive fracture model has proven to be effective in simulating crack initiation, branching, and propagation; however, capturing the cohesive fracture strength at smaller scales remains a significant challenge. This study introduces a novel approach that combines an energy-based star-convex decomposition cohesive phase-field fracture model with molecular dynamics simulations to explore the thickness dependency of nanocomposite mechanical properties. The proposed framework enables hierarchical modeling of carbon-nitride nanosheet-reinforced composites' mechanical and fracture behaviors. The developed model could elucidate complex fracture processes across different scales and highlight critical scaling effects. This methodology provides an efficient solution for uncovering hierarchical fracture mechanisms in reinforced nanocomposites, offering valuable insights into their fracture behavior and strengthening mechanisms.

cond-mat.mtrl-sci↗

arXiv2023

Boosting output performance of contact-separation mode triboelectric nanogenerators by adopting discontinuity and fringing effect: experiment and modelling studies

Triboelectric nanogenerators (TENGs) are promising self-powering supplies for a diverse range of intelligent sensing and monitoring devices, especially due to their capability of harvesting electric energy from low frequency and small-scale mechanical motions. Inspired by the fact that contact-separation mode TENGs with small contact areas harvest high electrical outputs due to fringing effect, this study employed discontinuity on the dielectric side of contact-separation mode TENGs to promote fringing electric fields for the enhancement of electrical outputs. The results reveal that the TENGs with more discontinuities show higher overall electric performance. Compared to pristine TENGs, the TENGs with cross discontinuities increased the surface charge by 50% and the power density by 114%. However, one should avoid generating discontinuities on tribonegative side of TENGs using metal blade within a positive-ion atmosphere due to the neutralization through electrically conductive metal blade. The computational simulation validated that the TENGs with discontinuities obtained higher electrical outputs, and further investigated the effect of discontinuity gap size and array distance on TENGs performance. This study has provided a promising method for the future design of TENGs using discontinuous structures.

physics.app-ph↗

arXiv2023

Isogeometric analysis of insoluble surfactant spreading on a thin film

In this paper we tackle the problem of surfactant spreading on a thin liquid film in the framework of isogeometric analysis. We consider a mathematical model that describes this phenomenon as an initial boundary value problem (IBVP) that includes two coupled fourth order partial differential equations (PDEs), one for the film height and one for the surfactant concentration. In order to solve this problem numerically, it is customary to transform it into a mixed problem that includes at most second order PDEs. However, the higher-order continuity of the approximation functions in Isogeometric Analysis (IGA) allows us to deal with the weak form of the fourth order PDEs directly, without the need of resorting to mixed methods. We demonstrate numerically that the IGA solution is able to reproduce results obtained before with mixed approaches. Complex phenomena such as Marangoni-driven fingering instabilities triggered by perturbations are easily captured.

math.NA↗

arXiv2012

NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

math.NA↗