Related papers: Transfer Learning using Neural Ordinary Differenti…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…
Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…
Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Simulating physical systems using Partial Differential Equations (PDEs) has become an indispensible part of modern industrial process optimization. Traditionally, numerical solvers have been used to solve the associated PDEs, however…
Training a Deep Neural Network (DNN) from scratch requires a large amount of labeled data. For a classification task where only small amount of training data is available, a common solution is to perform fine-tuning on a DNN which is…
In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of…
Learning from small amounts of labeled data is a challenge in the area of deep learning. This is currently addressed by Transfer Learning where one learns the small data set as a transfer task from a larger source dataset. Transfer Learning…
Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…
Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to…
Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow…
Uncertainty-based deep learning models have attracted a great deal of interest for their ability to provide accurate and reliable predictions. Evidential deep learning stands out achieving remarkable performance in detecting…
In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are…
Federated learning is a distributed machine learning approach in which clients train models locally with their own data and upload them to a server so that their trained results are shared between them without uploading raw data to the…
Deep neural networks have shown promising results for various clinical prediction tasks. However, training deep networks such as those based on Recurrent Neural Networks (RNNs) requires large labeled data, significant hyper-parameter tuning…