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We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change…

Numerical Analysis · Mathematics 2024-10-21 Bahae-Eddine Madir , Francky Luddens , Corentin Lothodé , Ionut Danaila

Wire-arc directed energy deposition (DED) has emerged as a promising additive manufacturing (AM) technology for large-scale structural engineering applications. However, the complex thermal dynamics inherent to the process present…

Computational Engineering, Finance, and Science · Computer Science 2025-07-15 Michael Ryan , Mohammad Hassan Baqershahi , Hessamoddin Moshayedi , Elyas Ghafoori

In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…

Machine Learning · Computer Science 2025-10-21 Kai-liang Lu

Obtaining dynamics models is essential for robotics to achieve accurate model-based controllers and simulators for planning. The dynamics models are typically obtained using model specification of the manufacturer or simple numerical…

Robotics · Computer Science 2021-10-26 Michael Lutter , Johannes Silberbauer , Joe Watson , Jan Peters

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This…

Computational Physics · Physics 2025-11-27 Tingkai Xue , Chin Chun Ooi , Zhengwei Ge , Fong Yew Leong , Hongying Li , Chang Wei Kang

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…

Systems and Control · Electrical Eng. & Systems 2023-11-13 Jochen Stiasny , Spyros Chatzivasileiadis

Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural…

Fluid Dynamics · Physics 2023-10-04 Nilam Tathawadekar , Nguyen Anh Khoa Doan , Camilo F. Silva , Nils Thuerey

We present a physics-constrained control-oriented deep learning method for modeling building thermal dynamics. The proposed method is based on the systematic encoding of physics-based prior knowledge into a structured recurrent neural…

Machine Learning · Computer Science 2020-11-13 Jan Drgona , Aaron R. Tuor , Vikas Chandan , Draguna L. Vrabie

The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…

The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is…

Quantum Physics · Physics 2023-01-09 Matthew Choi , Daniel Flam-Shepherd , Thi Ha Kyaw , Alán Aspuru-Guzik

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine…

Quantum Physics · Physics 2026-02-17 Ban Q. Tran , Nahid Binandeh Dehaghani , Rafal Wisniewski , Susan Mengel , A. Pedro Aguiar

We establish a theoretical framework for predicting friction and heat transfer coefficients in variable-properties forced air convection. Drawing from concepts in high-speed wall turbulence, which also involves significant temperature,…

Fluid Dynamics · Physics 2024-12-18 Davide Modesti , Sergio Pirozzoli

Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational…

Machine Learning · Computer Science 2025-04-21 Callen MacPhee , Yiming Zhou , Bahram Jalali

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Numerical Analysis · Mathematics 2024-07-15 Seungchan Ko , Sang Hyeon Park

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Numerical Analysis · Mathematics 2023-04-14 Shinhoo Kang , Emil M. Constantinescu

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Numerical Analysis · Mathematics 2020-06-16 Chengping Rao , Hao Sun , Yang Liu

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Machine Learning · Computer Science 2021-07-07 Sourav Dutta , Peter Rivera-Casillas , Orie M. Cecil , Matthew W. Farthing , Emma Perracchione , Mario Putti

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…

Machine Learning · Computer Science 2026-02-18 Siying Ma , Mehrdad M. Zadeh , Mauricio Soroco , Wuyang Chen , Jiguo Cao , Vijay Ganesh

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

Machine Learning · Computer Science 2025-07-29 Aarush Gupta , Kendric Hsu , Syna Mathod