arXiv subjects

Arun Govind Neelan

Publications and source records attributed to Arun Govind Neelan.

6 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Networks: Bridging the Divide Between Conservative and Non-Conservative Equations

In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture shocks and other discontinuities in compressible flows. Conversely, utilizing non-conservative forms often introduces significant errors near these discontinuities or results in smeared shocks. This dependency poses a considerable limitation, particularly as many PDEs encountered in complex physical phenomena, such as multi-phase flows, are inherently non-conservative. This inherent non-conservativity restricts the direct applicability of standard numerical solvers designed for conservative forms. This work aims to thoroughly investigate the sensitivity of Physics-Informed Neural Networks (PINNs) to the choice of PDE formulation (conservative vs. non-conservative) when solving problems involving shocks and discontinuities. We have conducted this investigation across a range of benchmark problems, specifically the Burgers equation and both steady and unsteady Euler equations, to provide a comprehensive understanding of PINNs capabilities in this critical area.

physics.flu-dyn↗

arXiv2026

AutoFOAM: The Self-Refining Autonomous OpenFOAM Agent

Computational Fluid Dynamics (CFD) plays an important role in modern engineering, but using open-source solvers such as OpenFOAM requires considerable knowledge and skills, as well as time-consuming configuration file setup. To reduce this burden, we propose AutoFOAM - a self-evolving large language model (LLM) agent that creates, evaluates, runs, and evolves its own OpenFOAM simulations based solely on natural-language instructions. Our model is pre-trained on the Qwen-coder 2.5-14B, which is then fine-tuned on 252 text prompts targeting 7 OpenFOAM solvers, 13 parametrized mesh templates, and a y plus-aware numerical policy. The crucial element of the algorithm is a sophisticated evolution loop composed of 7 stages. To prevent model degeneration under repeated self-training, the agent employs three complementary anti-collapse streams: RAG-augmented retry context, surgical dictionary-level patching, and prompt-diversity paraphrasing. By bridging generative artificial intelligence with rigorous fluid simulations, AutoFOAM accelerates rapid prototyping and democratizes advanced CFD workflows.

cs.AI↗

arXiv2026

Revisiting Conservativeness in Fluid Dynamics: Failure of Non-Conservative PINNs and a Path-Integral Remedy

The choice between conservative and non-conservative formulations is a fundamental dilemma in CFD. While non-conservative forms offer intuitive modeling in primitive variables, they typically produce erroneous shock speeds. This paper critically analyzes these formulations, contrasting classical failures against the capabilities of Physics-Informed Neural Networks (PINNs). Using the Adaptive Weight and Viscosity (PINNs-AWV) architecture, we evaluate cases ranging from shallow water equations to unsteady 1D and 2D Euler equations. Results reveal a significant dichotomy: while PINNs-AWV restores physical fidelity in scalar and steady systems, standard non-conservative PINNs fail in unsteady systems like the Sod shock tube. We demonstrate this failure stems from non-vanishing source terms introduced by viscous regularization, which violate the Rankine--Hugoniot jump conditions. To resolve this, we implement a path-integral framework based on Dal Maso--LeFloch--Murat (DLM) theory. By incorporating path-consistent losses in PINNs (PI-PINN) and using path-conservative numerical schemes, we successfully recover correct shock speeds within non-conservative frameworks. Our results prove the path-integral approach provides a rigorous mathematical bridge for physical accuracy in both classical and machine learning solvers, enabling primitive-variable formulations in transient, high-speed simulations.

physics.flu-dyn↗

arXiv2026

Data-Driven Discovery of Sign-Indefinite Artificial Viscosity for Linear Convection -- A Space-Time Reconvolution Perspective

Artificial viscosity is traditionally interpreted as a positive, spatially acting regularization introduced to stabilize numerical discretizations of hyperbolic conservation laws. In this work, we report a data-driven discovery that motivates a reinterpretation of this classical view. We consider the linear convection equation discretized using an unstable FTCS scheme augmented with a learnable artificial viscosity. Using automatic differentiation and gradient-based optimization, the viscosity field is inferred by minimizing the error with respect to the exact solution, without imposing any sign constraints. The optimized viscosity consistently becomes locally negative near extrema, while the numerical solution remains stable and nearly exact. This behavior is not readily explained within classical modified equation analysis and Lax-Wendroff-type arguments, which predict a strictly positive effective viscosity. To resolve this apparent contradiction, we reinterpret artificial viscosity as a space-time closure that compensates unresolved truncation errors while enforcing entropy stability through global dissipation balance rather than pointwise positivity. Within this framework, the Lax-Wendroff scheme corresponds to a degenerate projection in which temporal truncation errors are eliminated and reintroduced as spatial diffusion. We show that entropy stability constrains the integrated dissipation budget rather than the pointwise sign of spatial viscosity. As a result, locally negative viscosity naturally emerges as a numerical reconvolution operator that compensates for dispersive truncation errors. Negative viscosity is therefore not an unphysical diffusion process, but a scheme- and grid-dependent correction mechanism.

math.NA↗

arXiv2026

Event-Level Probabilistic Prediction of Extreme Rainfall over India Using Physics-Gated Latent Dynamics

Extreme rainfall over the Indian monsoon region poses severe societal and infrastructural risks but remains difficult to predict at daily time scales due to stochastic convective triggering and multiscale atmospheric interactions. While large-scale atmospheric fields provide important environmental context, their ability to localize extreme rainfall events is fundamentally limited. In this study, we examine how large-scale atmospheric information from ERA5 reanalysis can be leveraged for event-level probabilistic prediction of daily rainfall extremes over India. We compare an adaptive ConvLSTM baseline with a proposed Physics-Gated Latent Ordinary Differential Equation (PG-LODE) framework, which models atmospheric evolution as a continuous-time latent process whose dynamics are explicitly modulated by a physics-based gating mechanism under convectively unstable conditions. Extreme events are defined using the local 95th percentile of the India Meteorological Department gridded rainfall dataset during the June to September monsoon season. Pixel-wise evaluation shows limited skill for both models due to spatial displacement errors, whereas event-level tile-based verification reveals a clear performance contrast. The ConvLSTM remains highly conservative, detecting only 27 percent of extreme events, while PG-LODE achieves near-complete detection with a substantially higher critical success index and a moderate false alarm rate. These results demonstrate that physics-gated continuous-time latent dynamics offer a robust pathway for translating large-scale atmospheric predictability into reliable assessments of extreme rainfall risk.

math.NA↗

arXiv2023

Von Neumann Stability Analysis for Multi-level Multi-step Methods

Von Neumann stability analysis, a well-known Fourier-based method, is a widely used technique for assessing stability in numerical computations. However, as noted in "Numerical Solution of Partial Differential Equations: Finite Difference Methods" by Smith (1985, pp. 67-68), this approach faces limitations when applied to multi-level methods employing schemes with more than two levels. In this study, we aim to extend the applicability of Von Neumann stability analysis to multi-level methods. An alternative method closely related to Von Neumann stability analysis is the Approximate Dispersion Relation (ADR) analysis. In this work, we not only explore ADR analysis but also introduce various ADR analysis variants while examining their inherent limitations so that other researchers can improve the analysis before using that in their work. Furthermore, we propose an innovative strategy for reducing dissipation, optimizing it through the use of an evolutionary algorithm. Our findings demonstrate that our proposed method yields minimal errors when compared to other advection equation schemes, both in one and two spatial dimensions.

math.NA↗