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Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…

The power law has been observed in the degree distributions of many biological neural networks. Sparse deep neural networks, which learn an economical representation from the data, resemble biological neural networks in many ways. In this…

Self-models have been a topic of great interest for decades in studies of human cognition and more recently in machine learning. Yet what benefits do self-models confer? Here we show that when artificial networks learn to predict their…

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization. Partially unknown power line properties can render model-based approaches unsuitable. With…

Evolution has resulted in highly developed abilities in many natural intelligences to quickly and accurately predict mechanical phenomena. Humans have successfully developed laws of physics to abstract and model such mechanical phenomena.…

The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…

Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…

Like a scientist or a playing child, PowerPlay not only learns new skills to solve given problems, but also invents new interesting problems by itself. By design, it continually comes up with the fastest to find, initially novel, but…

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…

We present an approach to cosmology in which the Universe learns its own physical laws. It does so by exploring a landscape of possible laws, which we express as a certain class of matrix models. We discover maps that put each of these…

We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern'…

The optimal design of neural networks is a critical problem in many applications. Here, we investigate how dynamical systems with polynomial nonlinearities can inform the design of neural systems that seek to emulate them. We propose a…

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…

Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…

We present a weight similarity measure method that can quantify the weight similarity of non-convex neural networks. To understand the weight similarity of different trained models, we propose to extract the feature representation from the…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…

Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…