Related papers: Model-free Data-Driven simulation of inelastic mat…
Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series without imposing assumptions on the underlying stochastic dynamics. Though in this sense generative market simulation is…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
This work presents a data-driven magnetostatic finite-element solver that is specifically well-suited to cope with strongly nonlinear material responses. The data-driven computing framework is essentially a multiobjective optimization…
We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
Computational fluid dynamics models based on Reynolds-averaged Navier--Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant…
The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for…
Despite the successful implementations of physics-informed neural networks in different scientific domains, it has been shown that for complex nonlinear systems, achieving an accurate model requires extensive hyperparameter tuning, network…
Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex…
The control and modeling of robot dynamics have increasingly adopted model-free control strategies using machine learning. Given the non-linear elastic nature of bionic robotic systems, learning-based methods provide reliable alternatives…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. In this work we extract nonlocal models from data, circumventing these challenges…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…