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This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A…

Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either…

Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…

Graph Neural Networks (GNNs) have enjoyed wide spread applications in graph-structured data. However, existing graph based applications commonly lack annotated data. GNNs are required to learn latent patterns from a limited amount of…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

Interconnected complex systems usually undergo disruptions due to internal uncertainties and external negative impacts such as those caused by harsh operating environments or regional natural disaster events. To maintain the operation of…

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…

This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs),…

We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

This thesis investigates unsupervised time series representation learning for sequence prediction problems, i.e. generating nice-looking input samples given a previous history, for high dimensional input sequences by decoupling the static…

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses,…

Graphs neural networks (GNNs) learn node features by aggregating and combining neighbor information, which have achieved promising performance on many graph tasks. However, GNNs are mostly treated as black-boxes and lack human intelligible…

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to…

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori}…

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing…