arXiv subjects

Shyamprasad Karagadde

Publications and source records attributed to Shyamprasad Karagadde.

3 recordsLinked to original sources

arXiv2026

A coupled Kolmogorov-Arnold Network and Level-Set framework for evolving interfaces

Kolmogorov-Arnold Networks (KANs) require significantly smaller architectures compared to multilayer perceptron (MLP)-based approaches, while retaining expressive power through spline-based activations. Moving boundary problems are ubiquitous in physical systems, whose numerical solutions are quite complex. We propose a shallow KAN framework combined with a Level-set formulation that directly approximates the temperature distribution $T(\mathbf{x},t)$ and the moving interface $Γ(t)$, enforcing the governing PDEs, phase equilibrium, and Stefan condition through physics-informed residuals. Numerical experiments in one and two dimensions show that the framework achieves accurate reconstructions of both temperature fields and interface dynamics, highlighting the potential of KANs as a compact and efficient alternative for moving boundary PDEs. First, we validate the model with semi-infinite analytical solutions. Subsequently, the model is extended to 2D using a level-set based formulation for interface propagation, which is solved within the KAN framework. This work demonstrates that KANs are capable of solving complex moving boundary problems without the need for measurement data.

math-ph↗

arXiv2024

A Physics Informed Neural Network (PINN) Methodology for Coupled Moving Boundary PDEs

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the components of deep learning. A large class of physical problems in materials science and mechanics involve moving boundaries, where interface flux balance conditions are to be satisfied while solving DEs. Examples of such systems include free surface flows, shock propagation, solidification of pure and alloy systems etc. While recent research works have explored applicability of PINNs for an uncoupled system (such as solidification of pure system), the present work reports a PINN-based approach to solve coupled systems involving multiple governing parameters (energy and species, along with multiple interface balance equations). This methodology employs an architecture consisting of a separate network for each variable with a separate treatment of each phase, a training strategy which alternates between temporal learning and adaptive loss weighting, and a scheme which progressively reduces the optimisation space. While solving the benchmark problem of binary alloy solidification, it is distinctly successful at capturing the complex composition profile, which has a characteristic discontinuity at the interface and the resulting predictions align well with the analytical solutions. The procedure can be generalised for solving other transient multiphysics problems especially in the low-data regime and in cases where measurements can reveal new physics.

cs.LG↗

arXiv2019

On the mechanism responsible for unconventional thermal behaviour during freezing

In this study, identical experiments of bottom-cooled solidification fluidic mixtures that exhibit faceted and dendritic microstructures were performed. The strength of compositional convection was correlated with the solidifying microstructure morphology, with the help of separate Rayleigh numbers in the mushy and bulk-fluid zones. While the dendritic solidification experienced a monotonic decrease in the bulk fluid temperature, solidification of the faceted case revealed an unconventional, anomalous temperature rise in the bulk liquid, at the initiation of the eutectic phase. Based on the bulk-liquid temperature profile, three distinct regimes of heat transfer were observed in the liquid over the course of solidification, namely - convection-dominated, transition, and conduction-dominated. The observations were analyzed and verified with the help of different initial compositions, as well as other mixtures that form faceted morphology upon freezing. The observed temperature rise was further ascertained by performing an energy balance in an indicative control volume ahead of the solid-liquid interface. The plausible mechanism behind the gain in temperature of the liquid during freezing was further generalized with the help of a simplified one-dimensional numerical model, and was extended to metals which are low Prandtl number mixtures. The study sheds new insights into the role of microstrostructural morphology in governing the transport phenomena in the bulk liquid.

cond-mat.soft↗