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Continuous-depth learning has recently emerged as a novel perspective on deep learning, improving performance in tasks related to dynamical systems and density estimation. Core to these approaches is the neural differential equation, whose forward passes are the solutions of an initial value problem parametrized by a neural network. Unlocking the full potential of continuous-depth models requires a different set of software tools, due to peculiar differences compared to standard discrete neural networks, e.g inference must be carried out via numerical solvers. We introduce TorchDyn, a PyTorch library dedicated to continuous-depth learning, designed to elevate neural differential equations to be as accessible as regular plug-and-play deep learning primitives. This objective is achieved by identifying and subdividing different variants into common essential components, which can be combined and freely repurposed to obtain complex compositional architectures. TorchDyn further offers step-by-step tutorials and benchmarks designed to guide researchers and contributors.
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box di
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been successfull
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an a