Related papers: Interpretable Polynomial Neural Ordinary Different…

Deep neural networks (DNNs) are powerful black-box predictors that have achieved impressive performance on a wide variety of tasks. However, their accuracy comes at the cost of intelligibility: it is usually unclear how they make their…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling.…

Deep networks for Monocular Depth Estimation (MDE) have achieved promising performance recently and it is of great importance to further understand the interpretability of these networks. Existing methods attempt to provide posthoc…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…

A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…

Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a…

Deep neural networks (DNNs) have shown exceptional performances in a wide range of tasks and have become the go-to method for problems requiring high-level predictive power. There has been extensive research on how DNNs arrive at their…

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their…

Inferring unbiased treatment effects has received widespread attention in the machine learning community. In recent years, our community has proposed numerous solutions in standard settings, high-dimensional treatment settings, and even…

Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that…

In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable…

This work focuses on deriving quantitative approximation error bounds for neural ordinary differential equations having at most quadratic nonlinearities in the dynamics. The simple dynamics of this model form demonstrates how expressivity…

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…

As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…