Related papers: An Enhanced V-cycle MgNet Model for Operator Learn…

Residual networks (ResNets) have been utilized for various computer vision and image processing applications. The residual connection improves the training of the network with better gradient flow. A residual block consists of few…

Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce…

Quantization is widely employed in both cloud and edge systems to reduce the memory occupation, latency, and energy consumption of deep neural networks. In particular, mixed-precision quantization, i.e., the use of different bit-widths for…

The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…

Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

We train deep residual networks with a stochastic variant of the nonlinear multigrid method MG/OPT. To build the multilevel hierarchy, we use the dynamical systems viewpoint specific to residual networks. We report significant speed-ups and…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

Training convolutional neural networks (CNNs) on high-resolution images is often bottlenecked by the cost of evaluating gradients of the loss on the finest spatial mesh. To address this, we propose Multiscale Gradient Estimation (MGE), a…

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of…

Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods…

This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral…

Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…

Numerical simulation is dominant in solving partial difference equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet…

Gradient-based meta-learning methods leverage gradient descent to learn the commonalities among various tasks. While previous such methods have been successful in meta-learning tasks, they resort to simple gradient descent during…