Related papers: Neural network augmented wave-equation simulation

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

An elastic ideal 2D propagation medium, i.e., a membrane, can be simulated by models discretizing the wave equation on the time-space grid (finite difference methods), or locally discretizing the solution of the wave equation (waveguide…

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

This paper considers the problem of sequential fusion of predictions from neural networks (NN) and fusion of predictions from multiple NN. This fusion strategy increases the robustness, i.e., reduces the impact of one incorrect…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

Summary: Errors in gradient trajectories introduce significant artifacts and distortions in magnetic resonance images, particularly in non-Cartesian imaging sequences, where imperfect gradient waveforms can greatly reduce image quality.…

The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems but with low computational cost and low runtime. Various techniques have been explored within…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Diffusion models have marked a significant breakthrough in the synthesis of semantically coherent images. However, their extensive noise estimation networks and the iterative generation process limit their wider application, particularly on…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

Convolutional Neural Networks (CNNs) excel at image classification but remain vulnerable to common corruptions that humans handle with ease. A key reason for this fragility is their reliance on local texture cues rather than global object…

Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes,…

We introduce a precision polarization scheme for DNN inference that utilizes only very low and very high precision levels, assigning low precision to the majority of network weights and activations while reserving high precision paths for…