English
Related papers

Related papers: Thermodynamically-Informed Iterative Neural Operat…

200 papers

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

Numerical Analysis · Mathematics 2023-10-31 Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Machine Learning · Computer Science 2021-09-21 Alban Odot , Ryadh Haferssas , Stéphane Cotin

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Machine Learning · Computer Science 2025-09-26 Yichen Song , Yalun Wu , Yunbo Wang , Xiaokang Yang

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Machine Learning · Computer Science 2025-11-06 Gang Bao , Yaohua Zang

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

Numerical Analysis · Mathematics 2025-09-17 Fabian Kröpfl , Daniel Peterseim , Elisabeth Ullmann

In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…

Computational Engineering, Finance, and Science · Computer Science 2022-05-26 Wenhao Ding , Qing He , Hanghang Tong , Ping Wang

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

Machine Learning · Computer Science 2024-10-15 Chuanqi Chen , Jin-Long Wu

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…

Machine Learning · Computer Science 2026-02-16 Heechang Kim , Qianying Cao , Hyomin Shin , Seungchul Lee , George Em Karniadakis , Minseok Choi

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Computational Engineering, Finance, and Science · Computer Science 2024-05-14 Gabriel Garayalde , Matteo Torzoni , Matteo Bruggi , Alberto Corigliano

For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…

Computational Engineering, Finance, and Science · Computer Science 2023-01-02 Congjie Wei , Jiaxin Zhang , Kenneth M. Liechti , Chenglin Wu

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Computational Engineering, Finance, and Science · Computer Science 2024-09-30 Matteo Calafà , Emil Hovad , Allan P. Engsig-Karup , Tito Andriollo

We present a hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems. The neural network takes a computer-aided design representation as input and predicts the electromagnetic…

Computational Engineering, Finance, and Science · Computer Science 2024-11-19 Merle Backmeyer , Stefan Kurz , Matthias Möller , Sebastian Schöps

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Machine Learning · Computer Science 2025-07-08 Weidong Wu , Yong Zhang , Lili Hao , Yang Chen , Xiaoyan Sun , Dunwei Gong

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

Machine Learning · Computer Science 2025-06-24 Jing Wang , Biao Chen , Hairun Xie , Rui Wang , Yifan Xia , Jifa Zhang , Hui Xu

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and…

Fluid Dynamics · Physics 2025-04-10 Sunan Zhao , Zhijie Li , Boyu Fan , Yunpeng Wang , Huiyu Yang , Jianchun Wang

Deterministic routing has emerged as a promising technology for future non-terrestrial networks (NTNs), offering the potential to enhance service performance and optimize resource utilization. However, the dynamic nature of network topology…

Networking and Internet Architecture · Computer Science 2024-01-24 Keyi Shi , Jingchao Wang , Hongyan Li , Kan Wang

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…

Materials Science · Physics 2024-08-28 Harikrishnan Vijayakumaran , Jonathan B. Russ , Glaucio H. Paulino , Miguel A. Bessa

A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…

Numerical Analysis · Mathematics 2020-07-22 Assyr Abdulle , Doghonay Arjmand , Edoardo Paganoni