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Networks representing social, biological, technological or other systems are often characterized by higher-order interaction involving any number of nodes. Temporal hypergraphs are given by ordered sequences of hyperedges representing sets…

Accurate and efficient thermal dynamics models of permanent magnet synchronous motors are vital to efficient thermal management strategies. Physics-informed methods combine model-based and data-driven methods, offering greater flexibility…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

Climate-economic modeling under uncertainty presents significant computational challenges that may limit policymakers' ability to address climate change effectively. This paper explores neural network-based approaches for solving…

We study the connection between a family of non-Hermitian Hamiltonians H and Hermitian ones H based on exact solutions. In general, for a dynamic process in a non-Hermitian system H, there always exists a parallel dynamic process governed…

The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…

Restricted Boltzmann Machines (RBM) have attracted a lot of attention of late, as one the principle building blocks of deep networks. Training RBMs remains problematic however, because of the intractibility of their partition function. The…

Most natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics…

Neuro-fuzzy networks (NFNs) are transparent, symbolic, and universal function approximations that perform as well as conventional neural architectures, but their knowledge is expressed as linguistic IF-THEN rules. Despite these advantages,…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…

Criticality can be exactly demonstrated in certain models of brain activity, yet it remains challenging to identify in empirical data. We trained a fully connected deep neural network to learn the phases of an excitable model unfolding on…

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions…

To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion,…

We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…

We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…