arXiv subjects

Siva Viknesh

Publications and source records attributed to Siva Viknesh.

4 recordsLinked to original sources

arXiv2026

Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks

Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients. Passive scalar fields, such as concentration or temperature, are advected by the same underlying velocity field and have the potential to uncover hidden flow physics metrics such as WSS. In this work, we demonstrate such reconstruction from spatially limited passive scalar observations using two fundamentally different inverse frameworks: a differentiable physics framework based on discrete adjoint, PDE-constrained optimization, which enforces the governing equations as hard constraints, and physics-informed neural networks (PINNs), which treat them as soft constraints. Benchmark problems include a 2D canonical backward-facing step (2D-BFS) and a 3D patient-specific stenotic coronary artery. For the 2D-BFS case, evaluated under three measurement scenarios (near-wall, far-field, and combined), PINN achieves high accuracy when near-wall data are available but fails when restricted to far-field measurements, whereas the differentiable physics approach recovers accurate WSS across all scenarios. In the 3D patient-specific case, the differentiable physics framework outperforms PINNs, yielding accurate WSS reconstruction. These results establish that measurement location and inverse formulation jointly determine reconstruction fidelity in scalar-based near-wall flow inference. The proposed framework opens a path toward estimation of near-wall hemodynamics from scalar transport data, with broader applicability to fluid flow problems where passive scalars can be observed.

physics.flu-dyn↗

arXiv2026

Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient surrogates remains an open challenge. We propose the DIfferentiable Autoencoding Neural Operator - DIANO, an autoencoding neural operator framework that constructs visualizable coarse-grid latent spaces for both dimensionality and geometric reduction across varying spatial discretizations, with governing equations enforced directly within the latent space. Built upon neural operators, DIANO achieves this through an encoding neural operator that spatially coarsens the high-dimensional input functions into the latent representation, and a decoding neural operator that reconstructs the original inputs via spatial refinement. We assess DIANO's latent representation and performance against baselines, including the Convolutional Neural Operator and standard autoencoders. Furthermore, a fully differentiable partial differential equation (PDE) solver is integrated as the sole input-output functional mapping operator within the latent space, enabling end-to-end training with governing physics prescribed a priori through parametric PDEs. Various PDE formulations are investigated, including the 2D unsteady advection-diffusion and the 3D Pressure--Poisson equation, revealing that the fidelity of the embedded PDE relative to the true physics governs the learned latent representation and reconstruction accuracy. Benchmark problems include flow past a 2D cylinder, flow through a 2D symmetric stenosed artery, and a 3D patient-specific coronary artery, showing accurate reconstruction of high-fidelity spatio-temporal fields through low-fidelity latent PDE evolution at reduced computational cost, while yielding coherent, spatially organized, and meaningful latent structures.

cs.LG↗

arXiv2025

ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identification

Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear Dynamics (SINDy) and symbolic regression, can extract governing equations from observational data; however, they also come with distinct advantages and disadvantages. This paper introduces a novel method within the SINDy framework, termed ADAM-SINDy, which synthesizes the strengths of established approaches by employing the ADAM optimization algorithm. This facilitates the simultaneous optimization of nonlinear parameters and coefficients associated with nonlinear candidate functions, enabling precise parameter estimation without requiring prior knowledge of nonlinear characteristics such as trigonometric frequencies, exponential bandwidths, or polynomial exponents, thereby addressing a key limitation of SINDy. Through an integrated global optimization, ADAM-SINDy dynamically adjusts all unknown variables in response to data, resulting in an adaptive identification procedure that reduces the sensitivity to the library of candidate functions. The performance of the ADAM-SINDy methodology is demonstrated across a spectrum of dynamical systems, including benchmark coupled nonlinear ordinary differential equations such as oscillators, chaotic fluid flows, reaction kinetics, pharmacokinetics, as well as nonlinear partial differential equations (wildfire transport). The results demonstrate significant improvements in identifying parameterized dynamical systems and underscore the importance of concurrently optimizing all parameters, particularly those characterized by nonlinear parameters. These findings highlight the potential of ADAM-SINDy to extend the applicability of the SINDy framework in addressing more complex challenges in dynamical system identification.

cs.LG↗

arXiv2025

Role of flow topology in wind-driven wildfire propagation

Wildfires propagate through intricate interactions between wind, fuel, and terrain, resulting in complex behaviors that pose challenges for accurate predictions. This study investigates the interaction between wind velocity topology and wildfire spread dynamics, aiming to enhance our understanding of wildfire spread patterns. We revisited the non-dimensionalizion of the governing combustion model by incorporating three distinct time scales. This approach revealed two new non-dimensional numbers, contrasting with the conventional non-dimensionalization that considers only a single time scale. Through scaling analysis, we analytically identified the critical determinants of transient wildfire behavior and established a state-neutral curve, indicating where initial wildfires extinguish for specific combinations of the identified non-dimensional numbers. Subsequently, a wildfire transport solver was developed using a finite difference method, integrating compact schemes and implicit-explicit Runge-Kutta methods. We explored the influence of stable and unstable manifolds in wind velocity on wildfire transport under steady wind conditions defined using a saddle-type fixed point flow, emphasizing the role of the non-dimensional numbers. Additionally, we considered the benchmark unsteady double-gyre flow and examined the effect of unsteady wind topology on wildfire propagation, and quantified the wildfire response to varying wind oscillation frequencies and amplitudes using a transfer function approach. The results were compared to Lagrangian coherent structures (LCS) used to characterize the correspondence of manifolds with wildfire propagation. The comprehensive approach of utilizing the manifolds computed from wind topology provides valuable insights into wildfire dynamics across diverse wind scenarios, offering a potential tool for improved predictive modeling and management strategies.

physics.flu-dyn↗