Related papers: BelNet: Basis enhanced learning, a mesh-free neura…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Many different deep networks have been used to approximate, accelerate or improve traditional image operators. Among these traditional operators, many contain parameters which need to be tweaked to obtain the satisfactory results, which we…

Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational…

Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has…

Nonlinear hyperspectral unmixing has recently received considerable attention, as linear mixture models do not lead to an acceptable resolution in some problems. In fact, most nonlinear unmixing methods are designed by assuming specific…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…

We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts:…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

Typically, loss functions, regularization mechanisms and other important aspects of training parametric models are chosen heuristically from a limited set of options. In this paper, we take the first step towards automating this process,…

Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…

We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…

The Boltzmann equation, a fundamental model in kinetic theory, describes the evolution of particle distribution functions through a nonlinear, high-dimensional collision operator. However, its numerical solution remains computationally…

The requirement of high spectrum efficiency puts forward higher requirements on frame synchronization (FS) in wireless communication systems. Meanwhile, a large number of nonlinear devices or blocks will inevitably cause nonlinear…

Finetuning a pretrained model has become a standard approach for training neural networks on novel tasks, resulting in fast convergence and improved performance. In this work, we study an alternative finetuning method, where instead of…