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Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and…

Machine Learning · Computer Science 2025-05-27 Ahmad Peyvan , Varun Kumar , George Em Karniadakis

Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks,…

Machine Learning · Computer Science 2026-04-06 Tiantian Sun , Jian Zu

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Machine Learning · Computer Science 2021-03-23 Sifan Wang , Hanwen Wang , Paris Perdikaris

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes.…

Machine Learning · Computer Science 2025-07-08 Kazuma Kobayashi , Jaewan Park , Qibang Liu , Seid Koric , Diab Abueidda , Syed Bahauddin Alam

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Machine Learning · Statistics 2019-07-08 Somdatta Goswami , Cosmin Anitescu , Souvik Chakraborty , Timon Rabczuk

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

Systems and Control · Electrical Eng. & Systems 2025-11-10 Ioannis Karampinis , Petros Ellinas , Johanna Vorwerk , Spyros Chatzivasileiadis

Traditional approaches based on finite element analyses have been successfully used to predict the macro-scale behavior of heterogeneous materials (composites, multicomponent alloys, and polycrystals) widely used in industrial applications.…

Materials Science · Physics 2022-11-24 Rajat Arora

Crystal plasticity (CP) simulations are a tool for understanding how microstructure morphology and texture affect mechanical properties and are an essential component of elucidating the structure-property relations. However, it can be…

Computational Engineering, Finance, and Science · Computer Science 2024-06-17 Junyan He , Deepankar Pal , Ali Najafi , Diab Abueidda , Seid Koric , Iwona Jasiuk

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can…

Machine Learning · Computer Science 2022-07-18 Saurabh Deshpande , Jakub Lengiewicz , Stéphane P. A. Bordas

This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…

Numerical Analysis · Mathematics 2022-02-16 Christian Moya , Shiqi Zhang , Meng Yue , Guang Lin

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

Machine Learning · Computer Science 2025-03-04 Zhaoxi Jiang , Fei Wang

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

Numerical Analysis · Mathematics 2024-08-09 Yameng Zhu , Jingrun Chen , Weibing Deng

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

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

Numerical Analysis · Mathematics 2024-02-27 Jae Yong Lee , Steffen Schotthöfer , Tianbai Xiao , Sebastian Krumscheid , Martin Frank

Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…

Machine Learning · Computer Science 2025-11-25 Yueqi Wang , Guang Lin

We propose a machine learning approach to address a key challenge in materials science: predicting how fractures propagate in brittle materials under stress, and how these materials ultimately fail. Our methods use deep learning and train…

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

Medical Physics · Physics 2024-12-23 Avisha Kumar , Xuzhe Zhi , Zan Ahmad , Minglang Yin , Amir Manbachi

This work presents a variational physics-informed deep learning framework for phase-field modelling of brittle crack propagation in anisotropic media. Previous Deep Ritz Method (DRM) approaches have focused on second-order, isotropic…

Computational Physics · Physics 2026-04-15 N. Plungė , P. Brommer , R. S. Edwards , E. G. Kakouris

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

Machine Learning · Computer Science 2024-02-14 Sung Woong Cho , Jae Yong Lee , Hyung Ju Hwang

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Computational Engineering, Finance, and Science · Computer Science 2026-04-10 Sumanta Roy , Stephen T. Castonguay , Pratanu Roy , Michael D. Shields