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Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in…

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor…

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Learned time-series models, whether continuous or discrete, are widely used for forecasting the states of dynamical systems but suffer from error accumulation in multi-step forecasts. To address this issue, we propose a Predictor-Corrector…

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

Learning curve extrapolation predicts neural network performance from early training epochs and has been applied to accelerate AutoML, facilitating hyperparameter tuning and neural architecture search. However, existing methods typically…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical…

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…

As artificial intelligence (AI) applications continue to expand in next-generation networks, there is a growing need for deep neural network (DNN) models. Although DNN models deployed at the edge are promising for providing AI as a service…

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…