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We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM…
This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
Finite element methods (FEM) for high-temperature superconducting (HTS) magnets become time-consuming at larger scales, restricting the rapid optimization of meter-scale REBCO solenoids. In this work, a surrogate model based on a fully…
Cantilevered elastic foils can undergo self-induced, large-amplitude flapping when subject to fluid flow, a widely observed phenomenon of fluid-structure interaction, from fluttering leaves or the movement of fish fins. When harnessed in…
Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-resolution training data. In this paper, we break this…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of…
In this paper, we present a deep surrogate model for learning the Green's function associated with the reaction-diffusion operator in rectangular domain. The U-Net architecture is utilized to effectively capture the mapping from source to…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
Simulation-based plasma scenario development, optimization and control are crucial elements towards the successful deployment of next-generation experimental tokamaks and Fusion power plants. Current simulation codes require extremely…
Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
This manuscript proposes an optimization framework to find the tailor-made functionally graded material (FGM) profiles for thermoelastic applications. This optimization framework consists of (1) a random profile generation scheme, (2) deep…
Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…
We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in $H^1$ to PDEs with weak solutions in $H(\textbf{curl})$ or $H(\textbf{div})$. To this end, we…
The aim of this study is to develop surrogate models for quick, accurate prediction of thrust forces generated through flapping fin propulsion for given operating conditions and fin geometries. Different network architectures and…