arXiv subjects

Danial Faghihi

Publications and source records attributed to Danial Faghihi.

15 recordsLinked to original sources

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↗

arXiv2026

Evidence-Guided Neural Architecture Selection under Uncertainty for Subject-Specific Blood Glucose Forecasting

Reliable neural architecture selection is an open challenge in time-series forecasting under limited, noisy, and heterogeneous data, where standard heuristic architecture design and validation approaches fail to ensure accurate and reliable prediction and generalization. We propose EVIDENT (EVidence-based IDEntification of Neural archiTectures), a framework for architecture selection that integrates Bayesian training, evidence-based ranking, and task-specific validation under uncertainty. The framework explores the candidate architecture pool and identifies the lowest-capacity model that satisfies a prescribed validation criterion. We demonstrate this method using temporal convolutional networks (TCNs) for individualized blood glucose forecasting in type 1 diabetes patients. The results show that EVIDENT systematically rejects both under- and over-parameterized TCN architectures on population-level diabetes data, while identifying models that generalize reliably to unseen patients. When multiple architectures are competitive, the framework further supports plausibility-weighted ensemble predictions that enhance predictive performance. Compared with a random-search baseline, EVIDENT identified smaller architectures with more consistent forecasting performance on unseen patients. These findings establish EVIDENT as a strategy to neural architecture discovery, enabling reliable model selection for high-consequence forecasting in data-limited and heterogeneous settings.

cs.LG↗

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

UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration

The goal of this paper is to demonstrate and address challenges related to all aspects of performing a complete uncertainty quantification analysis of a complicated physics-based simulation like a 2D slab burner direct numerical simulation (DNS). The UQ framework includes the development of data-driven surrogate models, propagation of parametric uncertainties to the fuel regression rate--the primary quantity of interest--and Bayesian calibration of the latent heat of sublimation and a chemical reaction temperature exponent using experimental data. Two surrogate models, a Gaussian Process (GP) and a Hierarchical Multiscale Surrogate (HMS) were constructed using an ensemble of 64 simulations generated via Latin Hypercube sampling. HMS is superior for prediction demonstrated by cross-validation and able to achieve an error < 15% when predicting multiscale boundary quantities just from a few far field inputs. Subsequent Bayesian calibration of chemical kinetics and fuel response parameters against experimental observations showed that the default values used in the DNS should be higher to better match measurements. This study highlights the importance of surrogate model selection and parameter calibration in quantifying uncertainty in predictions of fuel regression rates in complex combustion systems.

physics.comp-ph↗

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↗

arXiv2025

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↗

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↗

arXiv2023

A Scalable Algorithm for Multi-Material Design of Thermal Insulation Components Under Uncertainty

This work presents a scalable computational framework for optimal design under uncertainty with application to multi-material insulation components of building envelopes. The forward model consists of a multi-phase thermo-mechanical model of porous materials governed by coupled partial differential equations (PDEs). The design parameter (material porosity) is an uncertain and space-dependent field, resulting in a high-dimensional PDE-constrained optimization under uncertainty problem after finite element discretization. The robust design framework uses a risk-averse formulation consisting of the mean and variance of the design objective to achieve target thermal and mechanical performances and mitigate uncertainty. To ensure the efficiency and scalability of the solution, a second-order Taylor approximation of the mean and variance and the low-rank structure of the preconditioned Hessian of the design objective are leveraged, which uncovers the low effective dimension of the high-dimensional uncertain parameter space. Moreover, a gradient-based optimization method is implemented using the Lagrangian formalism to derive expressions for the gradient and Hessian with respect to the design and uncertain parameters. Finally, approximated $\ell_0$ regularization functions are utilized via a continuation numerical scheme to promote sparsity in the designed porosity. The framework's accuracy, efficiency, and scalability are demonstrated with numerical examples of a building envelope insulation scenario.

math.OC↗

arXiv2023

Technical Note: PDE-constrained Optimization Formulation for Tumor Growth Model Calibration

We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation (PDE) with unknown parameters (diffusivity and proliferation rate) being spatial fields. We use a dimension-independent globalized, inexact Newton Conjugate Gradient algorithm to solve the PDE-constrained optimization. The required gradient and Hessian actions are also presented using the adjoint method and Lagrangian formalism.

cs.CE↗

arXiv2022

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient > 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model predicted tumor shape.

cs.CE↗

arXiv2021

A Predictive Multiphase Model of Silica Aerogels for Building Envelope Insulations

This work develops a multiphase thermomechanical model of porous silica aerogel and implements an uncertainty analysis framework consisting of the Sobol methods for global sensitivity analyses and Bayesian inference using a set of experimental data of silica aerogel. A notable feature of this work is implementing a new noise model within the Bayesian inversion to account for data uncertainty and modeling error. The hyper-parameters in the likelihood balance data misfit and prior contribution to the parameter posteriors and prevent their biased estimation. The results indicate that the uncertainty in solid conductivity and elasticity are the most influential parameters affecting the model output variance. Also, the Bayesian inference shows that despite the microstructural randomness in the thermal measurements, the model captures the data with 2% error. However, the model is inadequate in simulating the stress-strain measurements resulting in significant uncertainty in the computational prediction of a building insulation component.

cond-mat.mtrl-sci↗

arXiv2020

A Predictive Discrete-Continuum Multiscale Model of Plasticity With Quantified Uncertainty

Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distributions of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error

cs.CE↗

arXiv2020

Moment Preserving Constrained Resampling with Applications to Particle-in-Cell Methods

In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical instabilities. We introduce an algorithm for particle resampling called Moment Preserving Contrained Resampling (MPCR). The general algorithm partitions the system space into smaller subsets and is designed to conserve any number of particle and grid quantities with a high degree of accuracy (i.e. machine accuracy). The resampling scheme can be integrated into any PIC code. The advantages of MPCR, including performance, accuracy, and stability, are presented by examining several numerical tests, including a use-case study in gyrokinetic fusion plasma simulations. The tests demonstrate that while the computational cost of MPCR is negligible compared to the nascent particle evolution in PIC methods, periodic particle resampling yields a significant improvement in the accuracy and stability of the results.

physics.plasm-ph↗

arXiv2018

Goal-Oriented Adaptive Modeling of Random Heterogeneous Media and Model-Based Multilevel Monte Carlo Methods

Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For specificity, the base models considered involve stochastic partial differential equations characterizing, for example, steady-state heat conduction in random heterogeneous materials and stochastic elastostatics problems in linear elasticity. The adaptive process involves generating a sequence of surrogate models defined on a partition of the solution domain into regular subdomains and then, based on estimates of the error in the QoIs, assigning homogenized effective material properties to some subdomains and full random fine scale properties to others, to control the error so as to meet a preset tolerance. New model-based Multilevel Monte Carlo (mbMLMC) methods are presented that exploit the adaptive sequencing and are designed to reduce variances and thereby accelerate convergence of Monte Carlo sampling. Estimates of cost and mean squared error of the method are presented. The results of several numerical experiments are discussed that confirm that substantial saving in computer costs can be realized through the use of controlled surrogate models and the associated mbMLMC algorithms.

math.NA↗

arXiv2017

A Probabilistic Design Method for Fatigue Life of Metallic Component

In the present study, a general probabilistic design framework is developed for cyclic fatigue life prediction of metallic hardware using methods that address uncertainty in experimental data and computational model. The methodology involves (i) fatigue test data conducted on coupons of Ti6Al4V material (ii) continuum damage mechanics based material constitutive models to simulate cyclic fatigue behavior of material (iii) variance-based global sensitivity analysis (iv) Bayesian framework for model calibration and uncertainty quantification and (v) computational life prediction and probabilistic design decision making under uncertainty. The outcomes of computational analyses using the experimental data prove the feasibility of the probabilistic design methods for model calibration in presence of incomplete and noisy data. Moreover, using probabilistic design methods result in assessment of reliability of fatigue life predicted by computational models.

cs.CE↗