arXiv subjects

Pratyush Kumar Singh

Publications and source records attributed to Pratyush Kumar Singh.

5 recordsLinked to original sources

arXiv2026

Technical Note: Continuum Theory of Mixture for Three-phase Thermomechanical Model of Fiber-reinforced Aerogel Composites

We present a thermodynamically consistent three-phase model for the coupled thermal transport and mechanical deformation of ceramic aerogel porous composite materials, which is formulated via continuum mixture theory. The composite comprises a solid silica skeleton, a gaseous fluid phase, and dispersed solid fibers. The thermal transport model incorporates the effects of meso- and macro-pore size variations due to the Knudsen effect, achieved by upscaling phonon transport relations to derive constitutive equations for the fluid thermal conductivity. The mechanical model captures solid-solid and solid-fluid interactions through momentum exchange between phases. A mixed finite element formulation is employed to solve the multiphase model, and numerical studies are conducted to analyze key features of the computational model.

cs.CE↗

arXiv2026

Dynamic Image-Informed Selection of Biomechanical Tumor Growth Models

Glioblastoma progression is strongly influenced by evolving mechanical interactions between the tumor and surrounding brain tissue. However, the extent to which finite-deformation mechanics and constitutive assumptions improve subject-specific prediction as tumor burden evolves remains unclear. We introduce a sequential Bayesian inference and dynamic model selection framework that assimilates longitudinal murine magnetic resonance imaging (MRI) data to calibrate spatially varying tumor diffusivity, proliferation rate, and tissue stiffness in biomechanical tumor growth models. Competing formulations were compared at each imaging time, including reaction-diffusion without mechanics and reaction-diffusion coupled to linear elasticity or hyperelastic mechanics, using posterior model plausibility to adapt model choice for individualized one-scan-ahead prediction as new MRI scans are acquired. Across the studied animals, mechanically coupled models were consistently more plausible than the uncoupled reaction-diffusion model, and the evolution of model plausibility indicated an increasing role of mass effect and stress-mediated feedback of tumor growth during progression. While linear and hyperelastic coupled tumor growth models often produced similar tumor morphology, they yield distinct stress, deformation, and inferred stiffness fields, with the hyperelastic formulation often receiving higher posterior plausibility at later imaging times. These results indicate that, within the present longitudinal murine dataset, mechanical coupling is favored for image-informed glioma growth prediction and that constitutive assumptions should be evaluated sequentially for each subject rather than fixed a priori.

cs.CE↗

arXiv2025

Stochastic Deep Learning Surrogate Models for Uncertainty Propagation in Microstructure-Properties of Ceramic Aerogels

This study presents an integrated computational framework that, given synthesis parameters, predicts the resulting microstructural morphology and mechanical response of ceramic aerogel porous materials by combining physics-based simulations with deep learning surrogate models. Lattice Boltzmann simulations are employed to model microstructure formation during material synthesis process, while a finite element model is used to compute the corresponding mechanical properties. To overcome the prohibitive computational demands of repeated physics-based simulations required for characterizing the impact of microstructure randomness on mechanical properties, surrogate models are developed using Convolutional Neural Networks (CNNs) for both microstructure generation and microstructure-property mapping. CNN training is formulated as a Bayesian inference problem to enable uncertainty quantification and provide confidence estimates in surrogate model predictions, under limited training data furnished by physics-based simulations. Numerical results demonstrate that the microstructure surrogate model effectively generates microstructural images consistent with the morphology of training data across larger domains. The Bayesian CNN surrogate accurately predicts strain energy for in-distribution microstructures and its generalization capability to interpolated morphologies are further investigated. Finally, the surrogate models are employed for efficient uncertainty propagation, quantifying the influence of microstructural variability on macroscopic mechanical property.

cs.CE↗

arXiv2025

Chance-Constrained Optimal Design of Porous Thermal Insulation Systems Under Spatially Correlated Uncertainty

This paper presents a computationally efficient method for the optimal design of silica aerogel porous material systems, balancing thermal insulation performance with mechanical stability under stress concentrations. The proposed approach explicitly accounts for additive manufacturing uncertainties by modeling material porosity as a spatially correlated stochastic field within a multiphase finite element formulation. A risk-averse objective function, incorporating statistical moments of the design objective, is employed in conjunction with chance constraints that enforce mechanical stability by restricting the probability of exceeding critical stress thresholds. To mitigate the prohibitively high computational cost associated with the large-dimensional uncertainty space and Monte Carlo estimations of the objective function's statistical moments, a second-order Taylor expansion is utilized as a control variate. Furthermore, a continuation-based smoothing strategy is introduced to address the non-differentiability of the chance constraints, ensuring compatibility with gradient-based optimization. The resulting framework achieves computational scalability, remaining agnostic to the dimensionality of the stochastic design space. The effectiveness of the method is demonstrated through numerical experiments on two- and three-dimensional thermal break systems for building insulation. The results highlight the framework's capability to solve large-scale, chance-constrained optimal design problems governed by finite element models with uncertain design parameter spaces reaching dimensions in the hundreds of thousands.

cs.CE↗

arXiv2024

A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty

The widespread integration of deep neural networks in developing data-driven surrogate models for high-fidelity simulations of complex physical systems highlights the critical necessity for robust uncertainty quantification techniques and credibility assessment methodologies, ensuring the reliable deployment of surrogate models in consequential decision-making. This study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate), providing a systematic framework to uncover predictive neural network-based surrogate models within the large space of potential models, including various neural network classes and choices of architecture and hyperparameters. The framework is grounded in hierarchical Bayesian inferences and employs model validation tests to evaluate the credibility and prediction reliability of the surrogate models under uncertainty. Leveraging these principles, OPAL-surrogate introduces a systematic and efficient strategy for balancing the trade-off between model complexity, accuracy, and prediction uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two modeling problems, including the deformation of porous materials for building insulation and turbulent combustion flow for the ablation of solid fuels within hybrid rocket motors.

cs.CE↗