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This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Machine learning techniques have been widely employed as effective tools in addressing various engineering challenges in recent years, particularly for the challenging task of microstructure-informed materials modeling. This work provides a…
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…
Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do…
Hemodynamic parameters such as pressure and wall shear stress play an important role in diagnosis, prognosis, and treatment planning in cardiovascular diseases. These parameters can be accurately computed using computational fluid dynamics…
Deep learning, as a highly efficient method for metasurface inverse design, commonly use simulation data to train deep neural networks (DNNs) that can map desired functionalities to proper metasurface designs. However, the assumptions and…
Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…
Concurrent multiscale finite element analysis (FE2) is a powerful approach for high-fidelity modeling of materials for which a suitable macroscopic constitutive model is not available. However, the extreme computational effort associated…
We introduce a data-driven framework to automatically identify interpretable and physically meaningful hyperelastic constitutive models from sparse data. Leveraging symbolic regression, an algorithm based on genetic programming, our…
Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…
Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from…
The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…
This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical…
Modeling biological soft tissue is complex in part due to material heterogeneity. Microstructural patterns, which play a major role in defining the mechanical behavior of these tissues, are both challenging to characterize, and difficult to…
Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…