English
Related papers

Related papers: Neural Lumped Parameter Differential Equations wit…

200 papers

We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Machine Learning · Computer Science 2019-08-09 Yifan Sun , Linan Zhang , Hayden Schaeffer

We address the problem of robot guided assembly tasks, by using a learning-based approach to identify contact model parameters for known and novel parts. First, a Variational Autoencoder (VAE) is used to extract geometric features of…

Robotics · Computer Science 2024-12-12 Constantin Schempp , Christian Friedrich

Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…

Systems and Control · Computer Science 2019-12-04 Randi Wang , Vadim Shapiro

We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…

Optimization and Control · Mathematics 2023-08-25 Christian Aarset , Martin Holler , Tram Thi Ngoc Nguyen

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…

Machine Learning · Computer Science 2023-02-22 Jan N. Fuhg , Craig M. Hamel , Kyle Johnson , Reese Jones , Nikolaos Bouklas

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Methodology · Statistics 2025-07-01 Ziyuan Chen , Shunxing Yan , Fang Yao

Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…

Optimization and Control · Mathematics 2024-09-09 Christoph Plate , Carl Julius Martensen , Sebastian Sager

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…

Materials Science · Physics 2021-07-21 Carlos J. G. Rojas , Marco L. Bitterncourt , José L. Boldrini

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

Machine Learning · Computer Science 2021-09-17 Sutanu Bhowmick , Satish Nagarajaiah

In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…

Systems and Control · Electrical Eng. & Systems 2021-11-01 Tobias Thoma , Paul Kotyczka

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…

Numerical Analysis · Mathematics 2020-06-04 Henning Wessels , Christian Weißenfels , Peter Wriggers

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model…

Dynamical Systems · Mathematics 2023-05-15 Hikaru Hoshino , Yoshihiko Susuki , Takashi Hikihara

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Machine Learning · Computer Science 2025-01-22 Zihan Liu , Prashant N. Kambali , C. Nataraj

Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…

Machine Learning · Computer Science 2026-04-21 Eva van Tegelen , Taniya Kapoor , George A. K. van Voorn , Peter van Heijster , Ioannis N. Athanasiadis

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Numerical Analysis · Mathematics 2024-11-14 Weiheng Zhong , Hadi Meidani

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

Dynamical Systems · Mathematics 2022-06-22 Sandor Beregi , David A. W. Barton , Djamel Rezgui , Simon A. Neild

Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…

Computational Engineering, Finance, and Science · Computer Science 2025-04-08 Mingyuan Zhou , Haoze Song , Wenjing Ye , Wei Wang , Zhilu Lai