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Deep learning has been demonstrated with tremendous success in recent years. Despite so, its performance in practice often degenerates drastically when encountering out-of-distribution (OoD) data, i.e. training and test data are sampled…

Neural Ordinary Differential Equations (NODEs) are a new class of models that transform data continuously through infinite-depth architectures. The continuous nature of NODEs has made them particularly suitable for learning the dynamics of…

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections…

Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…

Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning. This study introduces a novel approach by applying the principles of gauge symmetries, a key…