Related papers: Can neural networks predict dynamics they have nev…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for…

Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning…

Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…

Discovering the neural mechanisms underpinning cognition is one of the grand challenges of neuroscience. However, previous approaches for building models of RNN dynamics that explain behaviour required iterative refinement of architectures…

Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can…

Known for their ability to identify hidden patterns in data, artificial neural networks are among the most powerful machine learning tools. Most notably, neural networks have played a central role in identifying states of matter and phase…

Accurate and efficient prediction of three-dimensional (3D) wall-bounded turbulent flows poses a significant challenge for machine learning methods, particularly in scenarios where flow field data are limited. Physics-informed neural…

Despite deep-learning being state-of-the-art for data-driven model predictions, it has not yet found frequent application in ecology. Given the low sample size typical in many environmental research fields, the default choice for the…

Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically,…

Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

We present a novel technique for assessing the dynamics of multiphase fluid flow in the oil reservoir. We demonstrate an efficient workflow for handling the 3D reservoir simulation data in a way which is orders of magnitude faster than the…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

We demonstrate a machine learning based approach which can learn the time-dependent electronic excitation dynamics of small molecules subjected to ion irradiation. Ensembles of recurrent neural networks are trained on data generated by…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved,…