Related papers: A Note on Dimensionality Reduction in Deep Neural …

With the remarkable success achieved by the Convolutional Neural Networks (CNNs) in object recognition recently, deep learning is being widely used in the computer vision community. Deep Metric Learning (DML), integrating deep learning with…

In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…

Current PINN implementations with sequential learning strategies often experience some weaknesses, such as the failure to reproduce the previous training results when using a single network, the difficulty to strictly ensure continuity and…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…

The interpretation of observations of atomic and molecular tracers in the galactic and extragalactic interstellar medium (ISM) requires comparisons with state-of-the-art astrophysical models to infer some physical conditions. Usually, ISM…

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

The resource requirements of deep neural networks (DNNs) pose significant challenges to their deployment on edge devices. Common approaches to address this issue are pruning and mixed-precision quantization, which lead to latency and memory…

Deep neural networks (DNNs) are ubiquitous in computer vision and natural language processing, but suffer from high inference cost. This problem can be addressed by quantization, which consists in converting floating point perations into a…

This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Deep neural networks (DNNs) have become a widely deployed model for numerous machine learning applications. However, their fixed architecture, substantial training cost, and significant model redundancy make it difficult to efficiently…

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…

In recent years, the Deep Learning Alternating Minimization (DLAM), which is actually the alternating minimization applied to the penalty form of the deep neutral networks training, has been developed as an alternative algorithm to overcome…

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…

Empirical Dynamic Modeling (EDM) is a nonlinear time series causal inference framework. The latest implementation of EDM, cppEDM, has only been used for small datasets due to computational cost. With the growth of data collection…

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…