arXiv subjects

Mitchell Daneker

Publications and source records attributed to Mitchell Daneker.

5 recordsLinked to original sources

arXiv2025

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. We propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework's uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

cs.LG↗

arXiv2024

ADEPT: A Noninvasive Method for Determining Elastic Parameters of Valve Tissue

Computer simulation of "virtual interventions" may inform optimal valve repair for a given patient prior to intervention. However, the paucity of noninvasive methods to determine in vivo mechanical parameters of valves limits the accuracy of computer prediction and their clinical application. To address this, we propose ADEPT: A noninvasive method for Determining Elastic Parameters of valve Tissue. In this work, we demonstrated its application to the tricuspid valve of a child. We first tracked valve displacements from open to closed frames within a 3D echocardiogram time sequence using image registration. Physics-informed neural networks were subsequently applied to estimate the nonlinear mechanical properties from first principles and reference displacements. The simulated model using these patient-specific parameters closely aligned with the reference image segmentation, achieving a mean symmetric distance of less than 1 mm. Our approach doubled the accuracy of the simulated model compared to the generic parameters reported in the literature.

q-bio.QM↗

arXiv2024

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elasticity map in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) by inferring the heterogeneous elasticity maps across three materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. We further applied our improved architecture to three additional examples of breast cancer tissue and extended our analysis to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Our selected network architecture consistently produced highly accurate estimations of heterogeneous elasticity maps, even when there was up to 10% noise present in the training data.

math.NA↗

arXiv2022

Effective Data Sampling Strategies and Boundary Condition Constraints of Physics-Informed Neural Networks for Identifying Material Properties in Solid Mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we developed efficient strategies to nonuniformly sample observational data. We also investigated different approaches to enforce Dirichlet boundary conditions as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

cond-mat.mtrl-sci↗

arXiv2022

Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce systems-biology informed neural networks for parameter estimation by incorporating the system of ODEs into the neural networks. To complete the workflow of system identification, we also describe structural and practical identifiability analysis to analyze the identifiability of parameters. We use the ultridian endocrine model for glucose-insulin interaction as the example to demonstrate all these methods and their implementation.

q-bio.QM↗