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Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences.…

Deep learning approaches have achieved unprecedented performance in visual recognition tasks such as object detection and pose estimation. However, state-of-the-art models have millions of parameters represented as floats which make them…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…

The recent advances in deep neural networks (DNNs) make them attractive for embedded systems. However, it can take a long time for DNNs to make an inference on resource-constrained computing devices. Model compression techniques can address…

Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…

Galactic systems are inherently multiphase, and understanding the roles and interactions of the various phases is key towards a more complete picture of galaxy formation and evolution. For instance, these interactions play a pivotal role in…

A conventional approach to train neural ordinary differential equations (ODEs) is to fix an ODE solver and then learn the neural network's weights to optimize a target loss function. However, such an approach is tailored for a specific…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Data-driven methods are becoming an essential part of computational mechanics due to their unique advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of…

Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…

This work evaluates the compression techniques on ConvNeXt models in image classification tasks using the CIFAR-10 dataset. Structured pruning, unstructured pruning, and dynamic quantization methods are evaluated to reduce model size and…

This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads,…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Deep neural networks (DNNs) have achieved unprecedented success in the field of artificial intelligence (AI), including computer vision, natural language processing and speech recognition. However, their superior performance comes at the…