arXiv subjects

K. Murari

Publications and source records attributed to K. Murari.

3 recordsLinked to original sources

arXiv2025

A residual weighted physics informed neural network for forward and inverse problems of reaction diffusion equations

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with two residual-weighting schemes to solve reaction diffusion equations and evaluate its performance on both forward and inverse problems. The approach computes weights proportional to the PDE residuals, rescales them, and incorporates these scaled residuals into the loss function, leading to more stable training. Furthermore, we establish generalized error bounds that account for training and quadrature errors, and we analyze the convergence and stability of the method. The proposed algorithms are validated through numerical experiments on nonlinear equations, supported by statistical error analysis. To further demonstrate the effectiveness of our methodology, we implemented PINN-based forward and inverse frameworks for the nonlinear equations and conducted a comparative analysis with the proposed RW-PINN approach.

math.NA↗

arXiv2024

Physics informed neural network for forward and inverse radiation heat transfer in graded-index medium

Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when applied to this medium. To address this issue, we apply physics-informed neural networks (PINNs)-based machine learning algorithms to simulate forward and inverse problems for this medium. We also provide the theoretical upper bounds. This theoretical framework is validated through numerical experiments of predefined and newly developed models that demonstrate the accuracy and robustness of the algorithms in solving radiation transport problems in the medium. The simulations show that the novel algorithm goes on with numerical stability and effectively mitigates oscillatory errors, even in cases with more pronounced variations in the refractive index.

math.NA↗

arXiv2014

Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz

A design for a compact x-ray light source (CXLS) with flux and brilliance orders of magnitude beyond existing laboratory scale sources is presented. The source is based on inverse Compton scattering of a high brightness electron bunch on a picosecond laser pulse. The accelerator is a novel high-efficiency standing-wave linac and RF photoinjector powered by a single ultrastable RF transmitter at x-band RF frequency. The high efficiency permits operation at repetition rates up to 1 kHz, which is further boosted to 100 kHz by operating with trains of 100 bunches of 100 pC charge, each separated by 5 ns. The entire accelerator is approximately 1 meter long and produces hard x-rays tunable over a wide range of photon energies. The colliding laser is a Yb:YAG solid-state amplifier producing 1030 nm, 100 mJ pulses at the same 1 kHz repetition rate as the accelerator. The laser pulse is frequency-doubled and stored for many passes in a ringdown cavity to match the linac pulse structure. At a photon energy of 12.4 keV, the predicted x-ray flux is $5 \times 10^{11}$ photons/second in a 5% bandwidth and the brilliance is $2 \times 10^{12}\mathrm{photons/(sec\ mm^2\ mrad^2\ 0.1\%)}$ in pulses with RMS pulse length of 490 fs. The nominal electron beam parameters are 18 MeV kinetic energy, 10 microamp average current, 0.5 microsecond macropulse length, resulting in average electron beam power of 180 W. Optimization of the x-ray output is presented along with design of the accelerator, laser, and x-ray optic components that are specific to the particular characteristics of the Compton scattered x-ray pulses.

physics.acc-ph↗