arXiv subjects

Deepak Mangal

Publications and source records attributed to Deepak Mangal.

3 recordsLinked to original sources

arXiv2026

Fast Stokesian Dynamics for Rigid Aggregates

We present a fast Stokesian dynamics (FSD) framework for the dynamics and rheology of suspensions of rigid aggregates. The method extends the sphere-level formulation of Fiore and Swan (2019) to multi-bead rigid bodies. Rigidity is enforced implicitly through geometric constraints, enabling stable and efficient time integration. We develop a block-triangular factorization preconditioner for the resulting saddle-point system. The approach combines an approximate inverse of the far-field mobility with a block-diagonal approximation of the Schur complement, enabling independent inversion of each aggregate sub-block via LU decomposition. The method is implemented as an open-source plugin for the HOOMD-blue software suite, and validated against benchmark problems, including doublet dynamics in shear flow, pair sedimentation, Brownian diffusion, and suspension rheology across dilute and structured regimes, accurately capturing both deterministic and stochastic behavior. The framework is further validated against experimental rheology of carbon black slurries, explicitly accounting for van der Waals cohesion, Hertzian contact, and tangential friction via enhanced lubrication. The simulations accurately reproduce the shear-thinning and high-shear viscous regimes. The method exhibits favorable GPU scaling for small system sizes, with decreasing runtime per bead prior saturation. A size-dependent Ewald splitting parameter accelerates simulations at low volume fractions, yielding up to an order-of-magnitude speedup compared to constant Ewald splitting. For larger systems, a constant Ewald splitting produces linear scaling with particle number, whereas the size-dependent choice leads to quadratic scaling due to increased far-field cost. Overall, the proposed framework enables accurate and scalable simulation of rigid aggregate suspensions in Stokes flow.

cond-mat.soft↗

arXiv2025

A detailed and comprehensive account of fractional Physics-Informed Neural Networks: From implementation to efficiency

Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations can be challenging considering the intricate details involved in their numerical solutions. Robust data-driven solutions hence can be of great interest for solving fractional differential equations. In the recent years, fractional physics-informed neural network has appeared as a platform for solving fractional differential equations and till now, efforts have been made to improve its performance. In this work, we present a fully detailed interrogation of fractional physics-informed neural networks with different foundations to solve different categories of fractional differential equations: fractional ordinary differntial equation, as well as two and three dimensional fractional partial differential equations. These equations are solved employing two numerical methods based on the Caputo formalism. We show that these platforms are generally able to accurately solve the equations with minor discrepancies at initial times. Nonetheless, since in Caputo formalism, the value of a fractional derivative at each point requires the function's value in all of its previous history, it is computationally burdensome. Here, we discuss strategies to improve accuracy of fractional physics-informed neural networks solutions without imposing heavy computational costs.

math.AP↗

arXiv2024

UniFIDES: Universal Fractional Integro-Differential Equation Solvers

The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific inquiry. However, a large body of natural phenomena incorporates memory effects that are best described via fractional integro-differential equations (FIDEs), in which the integral or differential operators accept non-integer orders. Addressing the challenges posed by nonlinear FIDEs is a recognized difficulty, necessitating the application of generic methods with immediate practical relevance. This work introduces the Universal Fractional Integro-Differential Equation Solvers (UniFIDES), a comprehensive machine learning platform designed to expeditiously solve a variety of FIDEs in both forward and inverse directions, without the need for ad hoc manipulation of the equations. The effectiveness of UniFIDES is demonstrated through a collection of integer-order and fractional problems in science and engineering. Our results highlight UniFIDES' ability to accurately solve a wide spectrum of integro-differential equations and offer the prospect of using machine learning platforms universally for discovering and describing dynamical and complex systems.

cs.LG↗