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Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty…

Computational Physics · Physics 2026-02-03 Hamidreza Eivazi , Jendrik-Alexander Tröger , Stefan Wittek , Stefan Hartmann , Andreas Rausch

AI-driven surrogate modeling has become an increasingly effective alternative to physics-based simulations for 3D design, analysis, and manufacturing. These models leverage data-driven methods to predict physical quantities traditionally…

Machine Learning · Computer Science 2025-05-06 Yu-hsuan Chen , Jing Bi , Cyril Ngo Ngoc , Victor Oancea , Jonathan Cagan , Levent Burak Kara

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Numerical Analysis · Mathematics 2023-05-08 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino

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

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…

Machine Learning · Computer Science 2022-02-08 Pengpeng Shi , Zhi Zeng , Tianshou Liang

Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…

Machine Learning · Computer Science 2025-12-23 Yiheng Zhang , Shaowu Wu , Yuanzhuo Xu , Jiajun Wu , Shang Xu , Steve Drew , Xiaoguang Niu

We propose a novel method for gradient-based optimization of black-box simulators using differentiable local surrogate models. In fields such as physics and engineering, many processes are modeled with non-differentiable simulators with…

Machine Learning · Computer Science 2020-09-30 Sergey Shirobokov , Vladislav Belavin , Michael Kagan , Andrey Ustyuzhanin , Atılım Güneş Baydin

Physics-based models play a key role in battery management, yet face challenges in real-time applications due to the high computational cost of solving coupled algebraic-partial differential equations. To accelerate model simulation, this…

Applied Physics · Physics 2026-01-06 Yi Zhuang , Yusheng Zheng , Yunhong Che , Remus Teodorescu

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

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Numerical Analysis · Mathematics 2019-12-17 Kailai Xu , Dongzhuo Li , Eric Darve , Jerry M. Harris

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis

Operator-based neural network architectures such as DeepONets have emerged as a promising tool for the surrogate modeling of physical systems. In general, towards operator surrogate modeling, the training data is generated by solving the…

Machine Learning · Computer Science 2024-02-28 Shivam Choubey , Birupaksha Pal , Manish Agrawal

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

Machine Learning · Computer Science 2021-04-19 Manuel A. Roehrl , Thomas A. Runkler , Veronika Brandtstetter , Michel Tokic , Stefan Obermayer

Nanophotonic device design aims to optimize photonic structures to meet specific requirements across various applications. Inverse design has unlocked non-intuitive, high-dimensional design spaces, enabling the discovery of high-performance…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Machine Learning · Computer Science 2023-10-02 Sidney Besnard , Frédéric Jurie , Jalal M. Fadili

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…

Machine Learning · Computer Science 2022-05-19 Wensheng Li , Chao Zhang , Chuncheng Wang , Hanting Guan , Dacheng Tao

This paper is a step-by-step, self-contained guide to the complete training cycle of a Physics-Informed Neural Network (PINN) -- a topic that existing tutorials and guides typically delegate to automatic differentiation libraries without…

Numerical Analysis · Mathematics 2026-04-21 Abdeladhim Tahimi

This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and…

Optimization and Control · Mathematics 2025-09-08 Jonathan R. Cangelosi , Matthias Heinkenschloss

This manuscript proposes an optimization framework to find the tailor-made functionally graded material (FGM) profiles for thermoelastic applications. This optimization framework consists of (1) a random profile generation scheme, (2) deep…

Computational Engineering, Finance, and Science · Computer Science 2024-08-27 Piyush Agrawal , Ihina Mahajan , Shivam Choubey , Manish Agrawal

We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs. In contrast to other machine learning (ML) approaches that…

Numerical Analysis · Mathematics 2025-06-24 Dimitrios G. Patsatzis , Lucia Russo , Constantinos Siettos