Related papers: A unified physics-informed generative operator fra…
Gravity inversion is the problem of estimating subsurface density distributions from observed gravitational field data. We consider the two-dimensional (2D) case, in which recovering density models from one-dimensional (1D) measurements…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…
Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…
Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…
Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…
This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While…
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…
This work introduces a paradigm for constructing parametric neural operators that are derived from finite-dimensional representations of Green's operators for linear partial differential equations (PDEs). We refer to such neural operators…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…
In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…
Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…
Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to…
Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions,…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…