arXiv subjects

Aryan Tyagi

Publications and source records attributed to Aryan Tyagi.

12 recordsLinked to original sources

arXiv2026

Spin Glass Mapping of the Parallel Minority Game

The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By encoding the agent choices as spin variables, the variance becomes a quadratic Hamiltonian with quenched random couplings $J_{ij}$ and random fields $h_i$. This mapping reveals inherent frustration and connects the PMG to the well developed theory of spin glasses, providing a new perspective on the frozen, sub-optimal configurations observed in stochastic strategies.

cond-mat.dis-nn↗

arXiv2026

Multiscale Structural Reliability Analysis in high dimensions with Tensor Trains and Physics-Augmented Neural Networks

Structural reliability evaluation for composites constitutes a fundamentally high-dimensional multiscale problem, as microscale material uncertainties must propagate to the macroscale and can be quantified as high-dimensional random fields. Conventional approaches are computationally intractable, as they rely on repeatedly solving coupled partial differential equation systems across scales while contending with the exponential complexity inherent in high-dimensional uncertainty quantification. This work introduces a scalable and physically consistent framework that addresses both bottlenecks simultaneously in the case of separation of scales and (anisotropic) linear elasticity. In particular, we couple a physics-augmented Voigt--Reuss Neural Network (VRNN) with the Deep Inverse Rosenblatt Transport (DIRT) method to estimate the posterior probability of structural failure. The VRNN is used to resolve the computationally expensive FE$^2$ scheme by providing a near-instantaneous evaluation of the homogenized stiffness tensor that is guaranteed to be symmetric, positive-definite, and strictly bounded within the Voigt--Reuss limits, enabling fast evaluation of the homogenized responses. The DIRT method constructs a sequence of functional tensor train approximations to efficiently store an approximation of the high-dimensional optimal importance sampling distribution for estimating the probability of failure. This mitigates the curse of dimensionality arising from the Karhunen--Lo\`eve expansion of the random fields. The framework is demonstrated on a three-dimensional heterogeneous benchmark problem, where the uncertainty in the microscale material properties is characterized by a Bayesian posterior distribution obtained from limited strain observations. Our results show that the proposed framework can provide low-variance estimates of failure probabilities in dimensions up to 150.

cs.CE↗

arXiv2026

Multiscale topology optimization of compressible and nearly incompressible anisotropic hyperelastic structures using physics-augmented neural networks

Multiscale topology optimization (TO) of hyperelastic materials remains computationally prohibitive due to the repeated solution of microscale boundary value problems. In this work, we present a concurrent multiscale topology optimization framework that overcomes this limitation by leveraging physics-augmented neural networks (PANNs) as surrogate constitutive models. The proposed approach enables the simultaneous optimization of macroscale material distribution and microscale descriptors, within a unified nonlinear finite strain setting. The surrogate models are constructed using input-specific neural networks (ISNNs) that enforce key physical principles directly within the architecture, including convexity and material symmetry through invariant-based representations and structural tensors. This ensures thermodynamic consistency and numerical stability while accurately representing homogenized anisotropic hyperelastic responses. The trained PANNs replace the microscale boundary value problem and provide efficient evaluations of stresses and consistent tangent moduli using analytical first and second derivatives of the neural network, enabling tractable large-scale multiscale optimization. The framework is demonstrated on representative microstructures exhibiting transversely isotropic, cubic anisotropic, and nearly incompressible isotropic behavior. The results show that the proposed method captures complex multiscale interactions and enables physically meaningful spatial tailoring of material properties, while significantly reducing computational cost compared to classical FE$^2$ approaches. These findings establish PANNs as a powerful tool for high-fidelity multiscale topology optimization of nonlinear anisotropic materials.

cs.CE↗

arXiv2025

Active-Absorbing Phase Transitions in the Parallel Minority Game

The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two families of microscopic decision rules: (i) agents update their choices based on instantaneous population in their alternative choices, and (ii) threshold-based activation that activates agents movement only after overcrowding density crossing a threshold. We measure time-dependent and steady state limits of activity $A(t)$, overcrowding fraction $F(t)$ as functions of the control parameter $g=N/D$, where $N$ is the number of agents and $D$ is the total number of sites. Instantaneous rules display mean-field directed-percolation (MF-DP) scaling with $\beta\approx1.00$, $\delta\approx0.5$, and $\nu_{\parallel}\approx2.0$. Threshold rules, however, produce a distinct non-mean-field universality class with $\beta\approx0.75$ and a systematic failure of dynamical scaling. We show that thresholding acts as a relevant perturbation to the critical behavior of the model. The results highlight how minimal cognitive features at the agent level fundamentally alter large-scale critical behavior in socio-economic and active systems.

cond-mat.stat-mech↗

arXiv2025

Deep Inverse Rosenblatt Transport for Structural Reliability Analysis

Accurately estimating the probability of failure in engineering systems under uncertainty is a fundamental challenge, particularly in high-dimensional settings and for rare events. Conventional reliability analysis methods often become computationally intractable or exhibit high estimator variance when applied to problems with hundreds of uncertain parameters or highly concentrated failure regions. In this work, we investigate the use of the recently proposed Deep Inverse Rosenblatt Transport (DIRT) framework for reliability analysis in solid mechanics. DIRT combines a TT decomposition with an inverse Rosenblatt transformation to construct a low-rank approximation of the posterior distribution, enabling efficient sampling and probability estimation in high-dimensional spaces. By representing the optimal importance density in the TT format, DIRT scales linearly in the input dimension while maintaining a compact, reusable surrogate of the target distribution. We demonstrate the effectiveness of the DIRT framework on three analytical reliability problems and one numerical example with dimensionality ranging from 2 to 250. Compared to established methods such as Bayesian updating with Subset Simulation (BUS-SuS), DIRT seems to lower the estimator variance while accurately capturing rare event probabilities for the benchmark problems of this study.

cs.CE↗

arXiv2024

Quantum-Based Salp Swarm Algorithm Driven Design Optimization of Savonius Wind Turbine-Cylindrical Deflector System

Savonius turbines, prominent in small-scale wind turbine applications operating under low-speed conditions, encounter limitations due to opposing torque on the returning blade, impeding high efficiency. A viable solution involves mitigating this retarding torque by directing incoming airflow through a cylindrical deflector. However, such flow control is highly contingent upon the location and size of the cylindrical deflector, and its angular velocity. This study introduces a novel design optimization framework tailored for enhancing the turbine-deflector system's performance. Leveraging surrogate models for computational efficiency, six different models were assessed, with Kriging selected for subsequent analysis based on its superior performance at approximating the relation between design parameters and objective function. The training data for the surrogate model and the flow field data around the system were obtained through Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations using a sliding mesh technique. An in-house code for the Quantum-based Salp Swarm Optimization (QSSO) algorithm was then employed to obtain design parameters corresponding to the peak power coefficient (Cp) for the stationary deflector-turbine system. Additionally, the QSSO algorithm was quantitatively compared with nine other competing algorithms. The optimized stationary deflector-turbine system showed an improvement of 26.94% in Cp at Tip Speed Ratio (TSR) of 0.9 compared to the baseline case. Further investigation into the effect of deflector rotational velocity ($\omega_d$) revealed significant improvements: 40.98% and 11.33% enhancement at $\omega_d$ = 3 rad/s, and 51.23% and 19.42% at $\omega_d$ = 40 rad/s, compared to configurations without a deflector and with the optimized stationary deflector, respectively at a TSR of 0.9.

physics.flu-dyn↗

arXiv2023

COPD-FlowNet: Elevating Non-invasive COPD Diagnosis with CFD Simulations

Chronic Obstructive Pulmonary Disorder (COPD) is a prevalent respiratory disease that significantly impacts the quality of life of affected individuals. This paper presents COPDFlowNet, a novel deep-learning framework that leverages a custom Generative Adversarial Network (GAN) to generate synthetic Computational Fluid Dynamics (CFD) velocity flow field images specific to the trachea of COPD patients. These synthetic images serve as a valuable resource for data augmentation and model training. Additionally, COPDFlowNet incorporates a custom Convolutional Neural Network (CNN) architecture to predict the location of the obstruction site.

cs.LG↗

arXiv2023

Optimization of Inverted Double-Element Airfoil in Ground Effect using Improved HHO and Kriging Surrogate Model

In the automotive industry, multi-element wings have been used to improve the aerodynamics of race cars. Multi-element wings can enhance a vehicle's handling and stability by reducing drag and increasing downforce, allowing it to corner more effectively and achieve higher speeds. Performance gains by utilizing the ground effect are highly sensitive to the wing setup. This study focuses on identifying the optimum design parameters for the airfoil to achieve the desired downforce and drag performance. The design parameters chosen are ride height, flap overlap, flap angle, and flap gap (the spacing between the flap and the main airfoil). These parameters are optimized for three different use cases: high downforce, low drag, and a setup with the highest airfoil efficiency. The force coefficient and flow field data were gathered using two-dimensional (2D) Reynolds Averaged Navier Stokes (RANS) simulations, with the turbulent flow modeled using the k-{\omega} Shear Stress Transport (SST) turbulence model. The Improved Harris Hawks Optimization (HHO) algorithm was used to obtain the optimal configuration of the double-element and the resulting designs showed a significant improvement in downforce and drag performance compared to the baseline designs. Improved HHO was further compared with other state-of-the-art algorithms for assessing the algorithm's performance for a problem with highly non-linear behavior, where it was able to demonstrate its ability to obtain the optimal solutions more efficiently.

physics.flu-dyn↗

arXiv2023

Application of Response Surface Method and Genetic Algorithm in the Design of High-Efficiency Prototype Vehicle

Breakthroughs in aerodynamic optimization have made it possible to develop efficient modes of transport with lesser exploitation of valuable resources. This makes it crucial for technical professionals such as engineers and scientists to understand the methodologies behind carrying out such optimizations. A common approach towards improving the aerodynamic properties of a vehicle is to alter its physical shape, which has concurrently been a very strenuous process given the time consumed to remodel the vehicle for each simulation process. This research aims to tackle this problem by using intelligent techniques to automate the step-by-step process of remodeling the car and arriving at a final optimized solution with a significantly lower drag coefficient, a quantity used to measure the amount of drag force acting on a vehicle. This is achieved by assigning particular parameters to ensure guided improvement of the airfoil in a process known as parametrization, followed by implementing a response surface methodology primarily to circumvent the strenuous task of performing a large number of CFD simulations by employing surrogate models to generate a response surface between selected independent variables. Further, evolutionary algorithms such as Genetic Algorithm have gained momentum in the optimization studies carried out during product design by selecting the optimum parameters from the available design spaces on the basis of natural evolution. The proposed method of optimization has been successfully implemented on a prototype vehicle with an improvement of 26.6% and 51.1% in the drag coefficient and drag area respectively.

physics.flu-dyn↗

arXiv2023

A Novel Framework for Optimizing Gurney Flaps using RBF Neural Network and Cuckoo Search Algorithm

Enhancing aerodynamic efficiency is vital for optimizing aircraft performance and operational effectiveness. It enables greater speeds and reduced fuel consumption, leading to lower operating costs. Hence, the implementation of Gurney flaps represents a promising avenue for improving airfoil aerodynamics. The optimization of Gurney flaps holds considerable ramifications for improving the lift and stall characteristics of airfoils in aircraft and wind turbine blade designs. The efficacy of implementing Gurney flaps hinges significantly on its design parameters, namely, flap height and mounting angle. This study attempts to optimize these parameters using a design optimization framework, which incorporates training a Radial Basis Function surrogate model based on CFD data from two-dimensional (2D) Reynolds-Averaged Navier-Stokes (RANS) simulations. The Cuckoo Search algorithm is then employed to obtain the optimal design parameters and compared with other competing optimization algorithms. The optimized Gurney flap configuration shows a notable improvement of 10.28% in Cl/Cd, with a flap height of 1.9%c and a flap mounting angle of -58 degrees. The study highlights the effectiveness of the proposed design optimization framework and furnishes valuable insights into optimizing Gurney flap parameters. The comparison of metaheuristic algorithms serves to enhance the study's contribution to Gurney flap design optimization.

physics.flu-dyn↗

arXiv2022

CKS: A Community-based K-shell Decomposition Approach using Community Bridge Nodes for Influence Maximization

Social networks have enabled user-specific advertisements and recommendations on their platforms, which puts a significant focus on Influence Maximisation (IM) for target advertising and related tasks. The aim is to identify nodes in the network which can maximize the spread of information through a diffusion cascade. We propose a community structures-based approach that employs K-Shell algorithm with community structures to generate a score for the connections between seed nodes and communities. Further, our approach employs entropy within communities to ensure the proper spread of information within the communities. We validate our approach on four publicly available networks and show its superiority to four state-of-the-art approaches while still being relatively efficient.

cs.SI↗

arXiv2022

Influence Maximization in Social Networks using Discretized Harris Hawks Optimization Algorithm and Neighbour Scout Strategy

Influence Maximization (IM) is the task of determining k optimal influential nodes in a social network to maximize the influence spread using a propagation model. IM is a prominent problem for viral marketing, and helps significantly in social media advertising. However, developing effective algorithms with minimal time complexity for real-world social networks still remains a challenge. While traditional heuristic approaches have been applied for IM, they often result in minimal performance gains over the computationally expensive Greedy-based and Reverse Influence Sampling-based approaches. In this paper, we propose the discretization of the nature-inspired Harris Hawks Optimisation meta-heuristic algorithm using community structures for optimal selection of seed nodes for influence spread. In addition to Harris Hawks intelligence, we employ a neighbour scout strategy algorithm to avoid blindness and enhance the searching ability of the hawks. Further, we use a candidate nodes-based random population initialization approach, and these candidate nodes aid in accelerating the convergence process for the entire populace. We evaluate the efficacy of our proposed DHHO approach on six social networks using the Independent Cascade model for information diffusion. We observe that DHHO is comparable or better than competing meta-heuristic approaches for Influence Maximization across five metrics, and performs noticeably better than competing heuristic approaches.

cs.SI↗