相关论文: DiffEqFlux.jl - A Julia Library for Neural Differe…

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…

In this work we systematically analyze general properties of differential equations used as machine learning models. We demonstrate that the gradient of the loss function with respect to to the hidden state can be considered as a…

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and…

Biological neural networks are often modeled as systems of coupled, nonlinear, ordinary or partial differential equations. The number of differential equations used to model a network increases with the size of the network and the level of…

In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing…

Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…

Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare…

Ai4EComponentLib.jl(Ai4EComponentLib) is a component-base model library based on Julia language, which relies on the differential equation solver DifferentialEquations.jl and the symbolic modeling tool Modelingtoolkit.jl. To handle problems…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…

Integrating computational fluid dynamics (CFD) solvers into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. In this…

We develop a framework for combining differentiable programming languages with neural networks. Using this framework we create end-to-end trainable systems that learn to write interpretable algorithms with perceptual components. We explore…

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural…

We present IncompressibleNavierStokes.jl, an open-source Julia package for solving the incompressible Navier--Stokes equations on staggered Cartesian grids. The package features matrix-free, hardware-agnostic kernels that are compiled from…

Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and…

JAX-Privacy is a library designed to simplify the deployment of robust and performant mechanisms for differentially private machine learning. Guided by design principles of usability, flexibility, and efficiency, JAX-Privacy serves both…