Related papers: Neural network augmented wave-equation simulation

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…

The characterization of particle diffusion is a classical problem in physics and probability theory. The field of microrheology is based on experiments in which microscopic tracer beads are placed into a non-Newtonian fluid and tracked…

As supported by abundant experimental evidence, neural networks are state-of-the-art for many approximation tasks in high-dimensional spaces. Still, there is a lack of a rigorous theoretical understanding of what they can approximate, at…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

Accurately localizing and segmenting obscured objects from faint light patterns beyond the field of view is highly challenging due to multiple scattering and medium-induced perturbations. Most existing methods, based on real-valued modeling…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

With the introduction of anti-aliased convolutional neural networks (CNN), there has been some resurgence in relooking the way pooling is done in CNNs. The fundamental building block of the anti-aliased CNN has been the application of…

Computational Fluid Dynamics (CFD) simulations are used for many air flow simulations including road vehicle aerodynamics. Numerical diffusion occurs when local flow direction is not aligned with the mesh lines and when there is a non-zero…

Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong…

Modulation recognition is a challenging task while performing spectrum sensing in a cognitive radio setup. Recently, the use of deep convolutional neural networks (CNNs) has shown to achieve state-of-the-art accuracy for modulation…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…