Related papers: Physics-Informed Neural Operators for Cardiac Elec…

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…

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…

Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth…

Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such…

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…

Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

Neural networks, while powerful, often lack interpretability. Physics-Informed Neural Networks (PINNs) address this limitation by incorporating physics laws into the loss function, making them applicable to solving Ordinary Differential…

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

Physics-Informed Neural Networks (PINNs) have recently been proposed to solve scientific and engineering problems, where physical laws are introduced into neural networks as prior knowledge. With the embedded physical laws, PINNs enable the…