Related papers: Non-Intrusive Hyperreduction by a Physics-Augmente…

We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

End-to-end autonomous driving has emerged as a dominant paradigm, yet its highly entangled black-box models pose significant challenges in terms of interpretability and safety assurance. To improve model transparency and training…

Model compression is crucial for deployment of neural networks on devices with limited computational and memory resources. Many different methods show comparable accuracy of the compressed model and similar compression rates. However, the…

Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively.…

The ability to train ever-larger neural networks brings artificial intelligence to the forefront of scientific and technical discoveries. However, their exponentially increasing size creates a proportionally greater demand for energy and…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However,…

A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…

Although deep neural networks have provided impressive gains in performance, these improvements often come at the cost of increased computational complexity and expense. In many cases, such as 3D volume or video classification tasks, not…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally…