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Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike…
This paper surveys studies on the use of neural networks for optimization in the training-data-free setting. Specifically, we examine the dataless application of neural network architectures in optimization by re-parameterizing problems…
Recurrent Neural Networks (RNNs) are commonly used for real-time processing, streaming data, and cases where the amount of training samples is limited. Backpropagation Through Time (BPTT) is the predominant algorithm for training RNNs;…
We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an…
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…
Recurrent Neural Networks (RNNs) are powerful tools for solving sequence-based problems, but their efficacy and execution time are dependent on the size of the network. Following recent work in simplifying these networks with model pruning…
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…
Recurrent neural networks (RNNs) have proved effective at one dimensional sequence learning tasks, such as speech and online handwriting recognition. Some of the properties that make RNNs suitable for such tasks, for example robustness to…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
Traditional Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) units operate on discrete time steps, often failing to capture the fluid temporal dynamics of real-world physical processes. Liquid Neural Networks (LNNs),…
Deep convolutional neural networks (CNNs) have brought breakthroughs in processing clinical electrocardiograms (ECGs), speaker-independent speech and complex images. However, typical CNNs require a fixed input size while it is common to…
The implicit solvent approach offers a computationally efficient framework to model solvation effects in molecular simulations. However, its accuracy often falls short compared to explicit solvent models, limiting its use in precise…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
Deep learning has been successfully adopted in mobile edge computing (MEC) to optimize task offloading and resource allocation. However, the dynamics of edge networks raise two challenges in neural network (NN)-based optimization methods:…
Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing…
Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful class of mesh-free numerical methods for solving partial differential equations (PDEs), particularly those involving complex geometries. In this work, we present an…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…