arXiv subjects

Rahul Halder

Publications and source records attributed to Rahul Halder.

6 recordsLinked to original sources

arXiv2026

Model Order Reduction of Cerebrovascular Hemodynamics Using POD_Galerkin and Reservoir Computing_based Approach

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D Computational Fluid Dynamics (CFD) snapshots of an idealised basilar artery bifurcation are first compressed into a low-dimensional latent space using Proper Orthogonal Decomposition (POD). We evaluate the performance of a POD-Galerkin (POD-G) model, which projects the Navier-Stokes equations onto the reduced basis, against a POD-Reservoir Computing (POD-RC) model that learns the temporal evolution of coefficients through a recurrent architecture. A multi-harmonic and multi-amplitude training signal is introduced to improve training efficiency. Both methodologies achieve computational speed-ups on the order of 10^2 to 10^3 compared to full-order simulations, demonstrating their potential as efficient and accurate surrogates for predicting flow quantities such as wall shear stress.

math.NA↗

arXiv2025

Coupling Physics Informed Neural Networks with External Solvers

The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in coupling with external forward solvers arise from the inability to access the discretized form (Finite difference, finite volume, finite element, etc.) of the governing equation directly through the network and to include them in its computational graph. This poses a significant challenge to conventional automatic-differentiation-based derivative computation of physics-based loss terms concerning the neural network hyperparameters if gradient-based optimization techniques are adopted. Therefore, we propose modifying the physics-based loss term to account for the residual arising from the external solver and to compute the derivative required for the optimization machinery. The proposed methodologies are demonstrated on benchmark full-order and reduced-order systems.

math.NA↗

arXiv2025

A Deep-Learning Enhanced Gappy Proper Orthogonal Decomposition Method for Conjugate Heat Transfer Problem

The current study aims to develop a non-intrusive Reduced Order Model (ROM) to reconstruct the full temperature field for a large-scale industrial application based on both numerical and experimental datasets. The proposed approach is validated against a domestic refrigerator. At the full order level, air circulation and heat transfer in fluid and between fluid and surrounding solids in the fridge were numerically studied using the Conjugated Heat Transfer (CHT) method to explore both the natural and forced convection-based fridge model followed by a parametric study-based on the ambient temperature, fridge fan velocity, and evaporator temperature. The main novelty of the current work is the introduction of a stable Artificial Neural Network (ANN) enhanced Gappy Proper Orthogonal Decomposition (GPOD) method which shows better performance than the conventional GPOD approach in such large-scale industrial applications. The full-order model is validated with the experimental results and the prediction accuracy of the surrogate model associated with different reduced-order approaches is compared with the benchmark numerical results or high-fidelity results. In our current work, we show that a prediction error of one degree centigrade and computational speed-up of 5000 is achieved even at a very sparse training dataset using the proposed deep-learning enhanced GPOD approach.

physics.flu-dyn↗

arXiv2024

A LSTM-enhanced surrogate model to simulate the dynamics of particle-laden fluid systems

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of application, the computational cost of the numerical simulations is very expensive. The use of the most modern high-performance computing infrastructures could help to mitigate such an issue but not completely fix it. In this work, we develop a non-intrusive data-driven reduced order model (ROM) for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The ROM is built using the proper orthogonal decomposition (POD) for the computation of the reduced basis space and the Long Short-Term Memory (LSTM) network for the computation of the reduced coefficients. We are interested in dealing both with system identification and prediction. The most relevant novelties rely on (i) a filtering procedure of the full-order snapshots to reduce the dimensionality of the reduced problem and (ii) a preliminary treatment of the particle phase. The accuracy of our ROM approach is assessed against the classic Goldschmidt fluidized bed benchmark problem. Finally, we also provide some insights about the efficiency of our ROM approach.

math.NA↗

arXiv2023

Physics Informed Neural Network Framework for Unsteady Discretized Reduced Order System

This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite difference scheme (whereas, any other discretization technique can be adopted), then projected on a reduced or latent space using the Proper Orthogonal Decomposition (POD)-Galerkin approach and next, the residual arising from discretized reduced order equation is considered as an additional loss penalty term alongside the data-driven loss term using different variants of deep learning method such as Artificial neural network (ANN), Long Short-Term Memory based neural network (LSTM). The LSTM neural network has been proven to be very effective for time-dependent problems in a purely data-driven environment. The current work demonstrates the LSTM network's potential over ANN networks in physics-informed neural networks (PINN) as well. The potential of using discretized governing equations instead of continuous form lies in the flexibility of input to the PINN. Different sizes of data ranging from small, medium to big datasets are used to assess the potential of discretized-physics-informed neural networks when there is very sparse or no data available. The proposed methods are applied to a pitch-plunge airfoil motion governed by rigid-body dynamics and a one-dimensional viscous Burgers' equation. The current work also demonstrates the prediction capability of various discretized-physics-informed neural networks outside the domain where the data is available or governing equation-based residuals are minimized.

math.NA↗

arXiv2023

Deep Learning-Driven Nonlinear Reduced-Order Models for Predicting Wave-Structure Interaction

Long Short-Term Memory (LSTM) network-driven Non-Intrusive Reduced Order Model (NROM) for predicting the dynamics of a floating box on the water surface in a wavemaker basin is addressed in this study. The ground truth or actual data for these wave-structure interactions (WSI) problems, namely box displacements and hydrodynamic forces and moments acting on the box due to wave interaction corresponding to a particular wave profile, are computed using the Smoothed Particle Hydrodynamics (SPH). The dimensionality of the system is first reduced using the Discrete Empirical Interpolation Method (DEIM) and the LSTM is applied to the reduced system resulting in a DEIM-LSTM network for developing a surrogate for prediction. The network is further enhanced by incorporating the physics information into the loss function resulting in a physics-informed LSTM (LSTM-PINN) for predicting the rigid body dynamics of box motion. The performance of predictions for these networks is assessed for the two-dimensional wave basin WSI problem as a proof-of-concept demonstration.

physics.flu-dyn↗