arXiv subjects

Biswanath Barman

Publications and source records attributed to Biswanath Barman.

3 recordsLinked to original sources

arXiv2026

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving forward and inverse partial differential equations (PDEs), but conventional real-valued PINNs (RV-PINNs) often suffer from spectral bias, limited expressivity, and reduced accuracy for high-frequency, oscillatory, and phase-dependent dynamics. In this work, we propose a generalized split complex-valued physics-informed neural network (SCV-PINN), in which network parameters and latent representations are defined in the complex domain. The framework employs split complex-valued activation functions by independently applying standard real-valued activations to the real and imaginary components, providing numerical stability, computational efficiency, and improved approximation capability. This formulation enables simultaneous learning of amplitude and phase information, enhancing the representation of nonlinear and oscillatory systems. Extensive ablation studies evaluate different split activation functions and collocation sampling strategies. The proposed framework is validated on forward and inverse PDE benchmarks including Burgers, Allen-Cahn, Korteweg-de Vries, nonlinear Schrodinger, Helmholtz, Poisson, Kovasznay flow (Re = 20), lid-driven cavity flow (Re = 100), the Lorenz system, inverse Burgers, inverse Navier-Stokes (Re = 100), and a three-dimensional Navier-Stokes Beltrami flow. For the Beltrami benchmark, SCV-PINN achieves a relative L2 error of 4.07 x 10^-5. Numerical results consistently demonstrate lower relative L2 errors and more accurate parameter identification than RV-PINNs and several existing PINN variants. The proposed SCV-PINN provides a robust and generalized extension of standard PINNs for complex-valued, multiscale, oscillatory, high-dimensional, and real-valued nonlinear PDEs.

physics.flu-dyn↗

arXiv2026

An Efficient Wavelet-based Physics Informed Residual Neural Networks for Flow Field Reconstruction with Extremely Sparse Data

This paper introduces wavelet-physics-informed residual neural networks (W-PIRNNs) to study complex fluid flow problems by reconstructing the flow field from highly sparse, supervised data. Our W-PIRNNs fundamentally integrate ResNet and employ the wavelet $W(t) = w_1 \sin(t) + w_2 \cos(t)$ as an activation function. Due to the vanishing and ballooning gradient problems associated with typical PINNs' deep networks, we implemented residual-based skip connections. Our W-PIRNNs, which integrate supervised data with physical principles, demonstrate efficacy even in scenarios of sparse or partial data, enabling the reconstruction of flow fields using merely $0.05\%$ velocity data for training. The wake flow around a circular cylinder served as the test case for our proposed technique, which depends exclusively on velocity data for training. This technique facilitates the precise reconstruction of velocity, pressure, streamlines, and vorticity, requiring fewer epochs and less processing time. Significantly, our proposed W-PIRNNs effectively resolve PDEs in both forward and inverse contexts. Burger's equation served as a test case for both the forward and inverse problem configurations. Our network calculates the diffusion or viscosity coefficient ($λ_2$) with an absolute error of $0.065\%$ and the convection coefficient ($λ_1$) with an absolute error of $0.002\%$. Furthermore, the Schrödinger equation is examined in the forward setting to assess the framework's ability to handle periodic boundary conditions. To the best of our knowledge, W-PIRNNs represent the first method capable of flow reconstruction using highly sparse supervised data, as well as reconstructing streamline and vorticity, and they effectively address both forward and inverse problems with high accuracy.

physics.flu-dyn↗

arXiv2026

A Simple but Efficient Transformer-Based Physics-Informed Neural Network for Incompressible Navier--Stokes Equations

Traditional computational fluid dynamics and physics-informed neural networks (PINNs) often suffer from high computational cost, mesh sensitivity, and reduced accuracy for strongly nonlinear and time-dependent flows. To address these limitations, we propose \textit{PhysicsFormer}, a simple and efficient Transformer-based physics-informed neural network framework for complex fluid flow simulations. The proposed architecture employs encoder--decoder multi-head attention to capture long-range temporal dependencies and enhance spatio-temporal information propagation. Unlike conventional multilayer perceptron-based PINNs, \textit{PhysicsFormer} utilizes pseudo-sequential spatio-temporal representations together with a dynamics-weighted loss formulation to improve convergence, stability, and predictive accuracy. Owing to its lightweight architecture and parallel learning strategy, the proposed framework achieves faster training and lower computational cost than existing Transformer-based PINN models. The performance of the proposed framework is demonstrated on the convection equation, Burgers' equation, lid-driven cavity flow at $Re=100$, and inverse Navier--Stokes and flow reconstruction problems for flow past a circular cylinder at $Re=100$ and $Re=3900$. For the inverse Navier--Stokes problem at $Re=100$, the proposed framework simultaneously reconstructs the flow field and identifies governing equation parameters with nearly $0\%$ absolute error under both clean and noisy data conditions. Furthermore, for the high-Reynolds-number case at $Re=3900$, \textit{PhysicsFormer} accurately reconstructs the velocity and pressure fields using only $25$ spatial measurements per snapshot over $100$ temporal snapshots. The obtained results demonstrate that \textit{PhysicsFormer} provides an accurate, robust, and computationally efficient framework for complex time-dependent fluid flow problems.

physics.flu-dyn↗