arXiv subjects

Ashish S. Nair

Publications and source records attributed to Ashish S. Nair.

5 recordsLinked to original sources

arXiv2026

BladeSDF : Unconditional and Conditional Generative Modeling of Representative Blade Geometries Using Signed Distance Functions

Generative AI has emerged as a transformative paradigm in engineering design, enabling automated synthesis and reconstruction of complex 3D geometries while preserving feasibility and performance relevance. This paper introduces a domain-specific implicit generative framework for turbine blade geometry using DeepSDF, addressing critical gaps in performance-aware modeling and manufacturable design generation. The proposed method leverages a continuous signed distance function (SDF) representation to reconstruct and generate smooth, watertight geometries with quantified accuracy. It establishes an interpretable, near-Gaussian latent space that aligns with blade-relevant parameters, such as taper and chord ratios, enabling controlled exploration and unconditional synthesis through interpolation and Gaussian sampling. In addition, a compact neural network maps engineering descriptors, such as maximum directional strains, to latent codes, facilitating the generation of performance-informed geometry. The framework achieves high reconstruction fidelity, with surface distance errors concentrated within $1\%$ of the maximum blade dimension, and demonstrates robust generalization to unseen designs. By integrating constraints, objectives, and performance metrics, this approach advances beyond traditional 2D-guided or unconstrained 3D pipelines, offering a practical and interpretable solution for data-driven turbine blade modeling and concept generation.

cs.LG↗

arXiv2025

E-PINNs: Epistemic Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify uncertainty in these networks. While techniques such as Bayesian PINNs (B-PINNs) provide a principled approach to capturing epistemic uncertainty through Bayesian inference, they can be computationally expensive for large-scale applications. In this work, we propose Epistemic Physics-Informed Neural Networks (E-PINNs), a framework that uses a small network, the epinet, to efficiently quantify epistemic uncertainty in PINNs. The proposed approach works as an add-on to existing, pre-trained PINNs with a small computational overhead. We demonstrate the applicability of the proposed framework in various test cases and compare the results with B-PINNs using Hamiltonian Monte Carlo (HMC) posterior estimation and dropout-equipped PINNs (Dropout-PINNs). In our experiments, E-PINNs achieve calibrated coverage with competitive sharpness at substantially lower cost. We demonstrate that when B-PINNs produce narrower bands, they under-cover in our tests. E-PINNs also show better calibration than Dropout-PINNs in these examples, indicating a favorable accuracy-efficiency trade-off.

cs.LG↗

arXiv2025

Physics-Based Machine Learning Closures and Wall Models for Hypersonic Transition-Continuum Boundary Layer Predictions

Modeling rarefied hypersonic flows remains a fundamental challenge due to the breakdown of classical continuum assumptions in the transition-continuum regime, where the Knudsen number ranges from approximately 0.1 to 10. Conventional Navier-Stokes-Fourier (NSF) models with empirical slip-wall boundary conditions fail to accurately predict nonequilibrium effects such as velocity slip, temperature jump, and shock structure deviations. We develop a physics-constrained machine learning framework that augments transport models and boundary conditions to extend the applicability of continuum solvers in nonequilibrium hypersonic regimes. We employ deep learning PDE models (DPMs) for the viscous stress and heat flux embedded in the governing PDEs and trained via adjoint-based optimization. We evaluate these for two-dimensional supersonic flat-plate flows across a range of Mach and Knudsen numbers. Additionally, we introduce a wall model based on a mixture of skewed Gaussian approximations of the particle velocity distribution function. This wall model replaces empirical slip conditions with physically informed, data-driven boundary conditions for the streamwise velocity and wall temperature. Our results show that a trace-free anisotropic viscosity model, paired with the skewed-Gaussian distribution function wall model, achieves significantly improved accuracy, particularly at high-Mach and high-Knudsen number regimes. Strategies such as parallel training across multiple Knudsen numbers and inclusion of high-Mach data during training are shown to enhance model generalization. Increasing model complexity yields diminishing returns for out-of-sample cases, underscoring the need to balance degrees of freedom and overfitting. This work establishes data-driven, physics-consistent strategies for improving hypersonic flow modeling for regimes in which conventional continuum approaches are invalid.

physics.flu-dyn↗

arXiv2025

Understanding Latent Timescales in Neural Ordinary Differential Equation Models for Advection-Dominated Dynamical Systems

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE systems employs a two-step strategy: a nonlinear dimensionality reduction using an autoencoder, followed by time integration in the latent space using a neural ODE. This study examines the applicability of such autoencoder-based neural ODE architectures to systems where advection dominates the dynamics. In addition to predictive performance, this work investigates the mechanisms behind model acceleration by analyzing how the autoencoder and neural ODE components influence latent system time-scales. These effects are quantified through eigenvalue analysis of dynamical system Jacobians. Specifically, the study evaluates the sensitivity of model accuracy and discovered latent time-scales to key training choices: decoupled versus end-to-end training, latent space dimensionality, and training trajectory length. A central finding is the crucial role of training trajectory length (i.e., the number of rollout steps included in the loss function), which directly impacts the recovered latent time-scales. Longer trajectories lead to larger limiting time-scales in the latent system, and the most accurate models are shown to capture the largest time-scales of the original system. These insights are demonstrated across a diverse set of unsteady, advection-driven fluid dynamics problems: (1) the Kuramoto-Sivashinsky equations, (2) hydrogen-air channel detonations governed by the compressible reacting Navier-Stokes equations, and (3) 2D atmospheric flows.

physics.flu-dyn↗

arXiv2023

Deep Learning Closure of the Navier-Stokes Equations for Transition-Continuum Flows

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one spatial dimension, their high dimensionality makes multi-dimensional Boltzmann calculations impractical for all but canonical configurations. It is therefore desirable to augment the Navier-Stokes equations in these regimes. We present an application of a deep learning method to extend the validity of the Navier-Stokes equations to the transition-continuum flows. The technique encodes the missing physics via a neural network, which is trained directly from Boltzmann solutions. While standard DL methods can be considered ad-hoc due to the absence of underlying physical laws, at least in the sense that the systems are not governed by known partial differential equations, the DL framework leverages the a-priori known Boltzmann physics while ensuring that the trained model is consistent with the Navier-Stokes equations. The online training procedure solves adjoint equations, constructed using algorithmic differentiation, which efficiently provide the gradient of the loss function with respect to the learnable parameters. The model is trained and applied to predict stationary, one-dimensional shock thickness in low-pressure argon.

physics.flu-dyn↗