相关论文: DPG loss functions for learning parameter-to-solut…

We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. We extend earlier works on meta-learning, and develop a gradient-based meta-learning algorithm for addressing diverse task…

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…

We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition…

Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…

End-to-End (E2E) learning-based concept has been recently introduced to jointly optimize both the transmitter and the receiver in wireless communication systems. Unfortunately, this E2E learning architecture requires a prior differentiable…

Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from…

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that…

The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to…

Image colorization aims to add color information to a grayscale image in a realistic way. Recent methods mostly rely on deep learning strategies. While learning to automatically colorize an image, one can define well-suited objective…

In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…

Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating…

Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization…

We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise…

Domain generalization (DG) strives to address distribution shifts across diverse environments to enhance model's generalizability. Current DG approaches are confined to acquiring robust representations with continuous features, specifically…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

This paper addresses supervised deep metric learning for open-set image retrieval, focusing on three key aspects: the loss function, mixup regularization, and model initialization. In deep metric learning, optimizing the retrieval…

Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.The schemes are based on a weak formulation of a…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…