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Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damage. The interaction of cracks with discontinuities, such as…

Machine Learning · Computer Science 2025-09-12 Elham Kiyani , Venkatesh Ananchaperumal , Ahmad Peyvan , Mahendaran Uchimali , Gang Li , George Em Karniadakis

This study focuses on addressing the challenges of solving analytically intractable differential equations that arise in scientific and engineering fields such as Hamilton-Jacobi-Bellman. Traditional numerical methods and neural network…

Numerical Analysis · Mathematics 2023-08-23 Daniel Sevcovic , Cyril Izuchukwu Udeani

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…

Computational Engineering, Finance, and Science · Computer Science 2023-02-28 Wei Li , Martin Z. Bazant , Juner Zhu

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Computational Engineering, Finance, and Science · Computer Science 2023-10-12 Junyan He , Shashank Kushwaha , Jaewan Park , Seid Koric , Diab Abueidda , Iwona Jasiuk

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Machine Learning · Computer Science 2025-12-24 Marco A. Iglesias , Michael. E. Causon , Mikhail Y. Matveev , Andreas Endruweit , Michael . V. Tretyakov

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Machine Learning · Computer Science 2024-11-12 Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Machine Learning · Computer Science 2025-08-05 Amogh Raj , Carol Eunice Gudumotou , Sakol Bun , Keerthana Srinivasa , Arash Sarshar

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

Fluid Dynamics · Physics 2026-01-14 Xiaofeng Liu , Yong G. Lai

Ground settlement prediction during the process of mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two paradigms are existing: a physics-driven approach utilizing process-oriented…

Computational Engineering, Finance, and Science · Computer Science 2025-08-07 Chen Xu , Ba Trung Cao , Yong Yuan , Günther Meschke

Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random…

Machine Learning · Computer Science 2022-06-23 Somayajulu L. N. Dhulipala , Ryan C. Hruska

Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of…

Computational Engineering, Finance, and Science · Computer Science 2025-07-04 Diab W. Abueidda , Mbebo Nonna , Panos Pantidis , Mostafa E. Mobasher

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM…

Machine Learning · Computer Science 2025-05-13 Bilal Ahmed , Yuqing Qiu , Diab W. Abueidda , Waleed El-Sekelly , Tarek Abdoun , Mostafa E. Mobasher

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

Machine Learning · Computer Science 2024-05-01 Katarzyna Michałowska , Somdatta Goswami , George Em Karniadakis , Signe Riemer-Sørensen

Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution…

Machine Learning · Computer Science 2022-12-12 Wuzhe Xu , Yulong Lu , Li Wang

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of…

Machine Learning · Statistics 2022-02-01 Shailesh Garg , Harshit Gupta , Souvik Chakraborty

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Machine Learning · Computer Science 2025-02-25 Luis Mandl , Somdatta Goswami , Lena Lambers , Tim Ricken

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

Particle-in-Cell (PIC) simulations are widely used for modeling plasma kinetics by tracking discrete particle dynamics. However, their computational cost remains prohibitively high, due to the need to simulate large numbers of particles to…

Computational Physics · Physics 2025-04-29 Jianhua Lv , Linlin Zhong

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…

Numerical Analysis · Mathematics 2024-09-05 Zhiwei Gao , Liang Yan , Tao Zhou