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Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

Numerical Analysis · Mathematics 2025-12-30 Allen Alvarez Loya , Daniel A. Serino , J. W. Burby , Qi Tang

Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…

Quantum Physics · Physics 2025-11-13 Giorgio Panichi , Sebastiano Corli , Enrico Prati

Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics…

Computational Engineering, Finance, and Science · Computer Science 2023-01-26 Vahidullah Tac , Kevin Linka , Francisco Sahli-Costabal , Ellen Kuhl , Adrian Buganza Tepole

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

Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation…

Quantum Physics · Physics 2025-09-10 Shahid Qamar , Rana Imran Mushtaq , Bo Li , Ho-Kin Tang

Accurate and efficient solutions of spatiotemporal partial differential equations (PDEs), such as phase-field models, are fundamental for understanding interfacial dynamics and microstructural evolution in materials science and fluid…

Computational Physics · Physics 2026-02-19 Mostafa Bamdad , Mohammad Sadegh Eshaghi , Cosmin Anitescu , Navid Valizadeh , Timon Rabczuk

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…

Computational Physics · Physics 2023-08-21 Shawn G. Rosofsky , Hani Al Majed , E. A. Huerta

Thermal errors in machine tools significantly impact machining precision and productivity. Traditional thermal error correction/compensation methods rely on measured temperature-deformation fields or on transfer functions. Most existing…

Machine Learning · Computer Science 2025-10-07 C. Coelho , M. Hohmann , D. Fernández , L. Penter , S. Ihlenfeldt , O. Niggemann

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Numerical Analysis · Mathematics 2020-02-26 Kailai Xu , Eric Darve

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

Computational Engineering, Finance, and Science · Computer Science 2026-04-16 Dibakar Roy Sarkar , Ján Drgoňa , Somdatta Goswami

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Machine Learning · Computer Science 2021-11-11 Yuhao Huang

Thermal dynamics modeling has been a critical issue in building heating, ventilation, and air-conditioning (HVAC) systems, which can significantly affect the control and maintenance strategies. Due to the uniqueness of each specific…

Machine Learning · Statistics 2019-11-11 Zhanhong Jiang , Young M. Lee

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

We explore the use of deep neural networks for nonlinear dimensionality reduction in climate applications. We train convolutional autoencoders (CAEs) to encode two temperature field datasets from pre-industrial control runs in the CMIP5…

Atmospheric and Oceanic Physics · Physics 2018-09-06 J. A. Saenz , N. Lubbers , N. M. Urban

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Machine Learning · Computer Science 2025-03-25 Edgar Torres , Jonathan Schiefer , Mathias Niepert

Heating, Ventilation, and Cooling (HVAC) systems are often the most significant contributor to the energy usage, and the operational cost, of large office buildings. Therefore, to understand the various factors affecting the energy usage,…

Systems and Control · Computer Science 2017-05-08 Joshua Gluck , Christian Koehler , Jennifer Mankoff , Anind Dey , Yuvraj Agarwal

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…

Numerical Analysis · Mathematics 2025-08-14 Junjie Yao , Yuxiao Yi , Liangkai Hang , Weinan E , Weizong Wang , Yaoyu Zhang , Tianhan Zhang , Zhi-Qin John Xu

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…

Machine Learning · Statistics 2021-03-31 Hassan Arbabi , Ioannis Kevrekidis
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