Related papers: Deep Convolutional Ritz Method: Parametric PDE sur…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Recently, surrogate models based on deep learning have attracted much attention for engineering analysis and optimization. As the construction of data pairs in most engineering problems is time-consuming, data acquisition is becoming the…

A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

The development of efficient surrogates for partial differential equations (PDEs) is a critical step towards scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the…

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed-form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…

Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

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…

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To…

Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…