相关论文: Kolmogorov n-Widths for Multitask Physics-Informed…

Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding…

We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving…

Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…

Metal additive manufacturing enables unprecedented design freedom and the production of customized, complex components. However, the rapid melting and solidification dynamics inherent to metal AM processes generate heterogeneous,…

Accurate temperature estimation of pouch cells with indirect liquid cooling is essential for optimizing battery thermal management systems for transportation electrification. However, it is challenging due to the computational expense of…

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…

Complex optimal design and control processes often require repeated evaluations of expensive objective functions and consist of large design spaces. Data-driven surrogates such as neural networks and Gaussian processes provide an attractive…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful mesh-free framework for solving ordinary and partial differential equations by embedding the governing physical laws directly into the loss function. However, their…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

This paper investigates model reduction methods for efficiently approximating the solution of parameter-dependent PDEs with a multi-parameter vector $\vec{\mu} \in \mathbb{R}^p$. In cases where the Kolmogorov $N$-width decays fast enough,…

Since its introduction in 2017, physics-informed deep learning (PIDL) has garnered growing popularity in understanding the evolution of systems governed by physical laws in terms of partial differential equations (PDEs). However, empirical…

A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approach exploits the local kernel theory which allows one to…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov…

State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…

We explore the data-parallel acceleration of physics-informed machine learning (PIML) schemes, with a focus on physics-informed neural networks (PINNs) for multiple graphics processing units (GPUs) architectures. In order to develop…

The ability to predict trajectories of surrounding agents and obstacles is a crucial component in many robotic applications. Data-driven approaches are commonly adopted for state prediction in scenarios where the underlying dynamics are…

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…

We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…

Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid…