Ganesh Sahadeo Meshram

Ganesh Sahadeo Meshram, Suman Chakraborty, Nishant Sinha et al.

In the complex domain of microfluidics systems, analysing fluid flow patterns through random-shaped circular microchannels is significantly challenging task. Conventional approach of solving such problems using computational fluid dynamics often incapable due to their intensive computational requirements and high simulation times. In this study, addressing these limitations, we introduce $μ$-FlowNet, a deep learning framework based on the adaptable U-Net autoencoders. This model provides a data-driven approach that enhances the prediction and mapping of random-shaped circular microchannels and their corresponding fluid flow patterns. The datasets required for the training of the model is generated by performing extensive simulations using conventional approach of computational fluid dynamics methods. The datasets are then pre-processed and accessed the required spatial and temporal features that are essential for the training. We have trained three different models based on U-Net framework namely, standard U-Net, T-Net, and U-Net with attention mechanism to compare the prediction accuracy and loss. The accuracy of the $μ$-FlowNet is compared using metrics of dice score and intersection over union and it shows that U-Net with attention mechanism shows the highest dice score and IoU of 0.9317 and 0.8731, respectively and shows the highest structural similarity as compared to standard U-Net and T-Net. This show that U-Net with attention mechanism serves best model to map the fluid flow pattern with random datasets on testing.

Ganesh Sahadeo Meshram, Partha Pratim Chakrabarti, Suman Chakraborty

Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid dynamic (CFD) simulations are prohibitively expensive, taking more than 18 to 24 hours for each transient computation. In this paper, Physics-Informed Laplace Operator Neural Network (PI-LNO) is introduced, representing a novel architecture where the Laplace integral transform function serves as a learned physics-informed functional basis. Extensive comparative benchmark studies were performed against five other state-of-the-art approaches: UNet, UNet with attention modules (UNet-AM), DeepONet, Physics-Informed UNet (PI-UNet), and Laplace Neural Operator (LNO). Through complex Laplace transforms, PI-LNO natively models the exponential transient dynamics of the spreading process. A TensorFlow-based PI-LNO is trained on multi-surface CFD data spanning contact angles $θ_s ε[20,160]$, employing a physics-regularized composite loss combining data fidelity (MSE, MAE, RMSE) with Navier-Stokes, Cahn-Hilliard, and causality constraints.

Ganesh Sahadeo Meshram, Partha Pratim Chakrabarti, Suman Chakraborty

We introduce a Lattice-Boltzmann-driven kinetic physics-informed neural network (K-PINN) for predictive modeling of droplet dynamics on structured surfaces, in which the discrete Boltzmann-BGK equation is incorporated into the learning framework. Different from traditional PINNs that are restricted by macroscopic continuum equations, the K-PINN framework is built on the mesoscopic kinetic level, in which the essential Lattice-Boltzmann physics is preserved in the data-efficient neural network. The K-PINN has been successfully employed for modeling non-trivial droplet phenomena such as contact pinning, anisotropic spreading, and capillary hysteresis on substrates of different morphologies, ranging from random roughness to periodic pillar structures. Moreover, strict physical consistency, such as mass conservation within 1.5%, is ensured in the K-PINN framework. Furthermore, the U-Net-based encoder-decoder structure of the K-PINN results in a 50-75% reduction in error compared to traditional neural networks, achieving almost perfect agreement with high-resolution Lattice-Boltzmann simulations $L_2$ ~ 0.021-0.026, $R^2$ ~ 0.999. Robust convergence of the K-PINN to diverse surface morphologies is ensured through curriculum learning and adaptive two-phase optimization. Upon convergence, the K-PINN can perform real-time prediction with over 104 evaluations per second. Through the combination of kinetic theory and physics-informed learning, this work establishes a new paradigm for fast, physically consistent modeling of multiphase flows on complex surfaces.

Ganesh Sahadeo Meshram, Partha Pratim Chakrabarti, Suman Chakraborty

In this study, we have explored an application of deep learning architecture of the U-Net model, originally designed for biomedical image segmentation, in a regression analysis aimed at predicting fluid flows through textured microchannels. The data for this analysis is generated using the lattice Boltzmann method through extensive simulations, capturing the intricate behaviors of fluid dynamics in a microscale environment. The raw simulation data was meticulously preprocessed to prepare it for training the U-Net model, ensuring that the input features and labels were appropriately formatted and normalized to optimize the learning process of the model. The U-Net model, with its inherent capability of capturing spatial hierarchies and producing better predictions, proved effective in this novel application. We have evaluated the performance of the model using metrics including MSE, RMSE, MAE, and $R^2$ scores. These metrics were crucial in assessing the accuracy and reliability of the model predictions. The results demonstrate that the U-Net model can predict fluid flows with high accuracy and less error, indicating its potential for broader applications in fluid dynamics and other fields requiring precise regression modeling. A parametric analysis of the U-Net with attention mechanism showed that the velocity field prediction is contingent upon the solid-fluid interaction parameter and surface wettability. The U-Net equipped with an attention mechanism predicts the velocity magnitude and components for textured microchannels with an average error of 5.18%, which upon optimization may subsequently lower to 2.1%. The U-Net model including an attention mechanism (U-Net AM) regularly surpasses the conventional U-Net model in all measures, evidencing enhanced accuracy and generalization.

Ganesh Sahadeo Meshram, Partha Pratim Chakrabarti, Suman Chakraborty

One of the biggest challenges in the optimization of micro-scale fluid transport phenomena is the prediction of unsteady fluid flow in the presence of rough channel walls. Even though the accuracy of available computational fluid dynamics (CFD) solvers such as the lattice Boltzmann method (LBM) is satisfactory, the computational cost of design exploration is very high due to the diverse range of geometries and flow regimes involved in microchannel flows. The present paper introduces a revolutionary concept of a ground-breaking physics-informed neural network (PINN) that utilizes sparse lattice Boltzmann data in combination with the Navier-Stokes equations for the prediction of unsteady fluid flow in fractal-rough microchannels. The roughness of the channel walls is represented by the Weierstrass-Mandelbrot function, considering the characteristics of the surface roughness in real-life problems. The constraints of the Navier-Stokes equations are incorporated in the loss function of the PINN concept for achieving accuracy at much lower computational costs of 150-200 times fewer data points. The validation of the accuracy of the reconstruction of the flow fields is carried out for different Reynolds numbers ranging from Re = 1 to 45 and different amplitude values of the rough channel walls ranging from 5 to 20 lattice units.