Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared classical numerical methods PINNs several advantages, example their ability provide mesh-free solutions of equations and carry out forward inverse modelling within the same optimisation problem. Whilst promising, key limitation date is that struggled accurately efficiently solve with large domains and/or multi-scale solutions, which crucial...

We propose a method for solving differential equations.• Our combines PINNs with multilevel domain decomposition.• approach significantly outperforms when multiscale problems.• Multilevel modeling improves accuracy by aiding communication between subdomains.

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving wave equation. Whilst PINNs have been successfully applied across many physical systems, equation presents unique challenges due to multi-scale, propagating and oscillatory nature its solutions, it is unclear how well they perform in this setting. a deep neural network learn solutions equation, using boundary condition as direct constraints loss function when training network. test approach by 2D acoustic...

Abstract. The simulation of seismic waves is a core task in many geophysical applications. Numerical methods such as finite difference (FD) modelling and spectral element (SEMs) are the most popular techniques for simulating waves, but disadvantages their computational cost prohibit use tasks. In this work, we investigate potential deep learning aiding solid Earth sciences. We present two neural networks which able to simulate response at multiple locations horizontally layered faulted 2-D...

Abstract The lunar permanently shadowed regions (PSRs) are expected to host large quantities of water-ice, which key for sustainable exploration the Moon and beyond. In near future, NASA other entities plan send rovers humans characterize water-ice within PSRs. However, there exists only limited information about small-scale geomorphology distribution ice PSRs because orbital imagery captured date lacks sufficient resolution and/or signal. this paper, we develop validate a new method...

Recently, learning-based approaches have achieved impressive results in the field of low-light image denoising. Some state art employ a rich physical model to generate realistic training data. However, performance these ultimately depends on realism model, and many works only concentrate everyday photography. In this work we present denoising approach for extremely images permanently shadowed regions (PSRs) lunar surface, taken by Narrow Angle Camera board Lunar Reconnaissance Orbiter...

Abstract The Artemis program will send crew to explore the south polar region of Moon, preceded by and integrated with robotic missions. One main scientific goals future exploration is characterization volatiles, which are concentrated in near regions permanent shadow. meter‐scale cryogeomorphology shadowed remains unknown, posing a potential risk missions that plan traverse or land them. Here, we deploy physics‐based, deep learning‐driven post‐processing tool produce high‐signal...

Physics Informed Neural Networks (PINNs) offer several advantages when compared to traditional numerical methods for solving PDEs, such as being a mesh-free approach and easily extendable inverse problems. One promising allowing PINNs scale multi-scale problems is combine them with domain decomposition; example, finite basis physics-informed neural networks (FBPINNs) replace the global PINN network many localised which are summed together approximate solution. In this work, we significantly...

We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the forward and inverse modeling of synthetic problem media, we applied it real experimental dataset which brine is injected at constant pressure drop into CO2 saturated naturally shale core plug. The exact spatial positions natural fractures dynamic in-situ distribution fluids were imaged using CT-scan setup. To targeted system, followed domain...

Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the needs obtained from relational database via feature extraction query, computation cost can prohibitive, as may (much) larger than total input relation size. This paper introduces Rk-means, or k -means algorithm, for clustering tuples without having access full matrix. As such, we avoid run expensive query and storing its output. Our algorithm leverages underlying structures in...

Abstract We investigate the use of unsupervised machine learning to understand and extract valuable information from thermal measurements lunar surface. train a variational autoencoder (VAE) reconstruct observed variations in surface temperature over 9 yr Diviner Lunar Radiometer Experiment data doing so learn fully data-driven thermophysical model The VAE defines probabilistic latent that assumes can be described by small set independent variables uses deep convolutional neural network...

Abstract. The simulation of seismic waves is a core task in many geophysical applications. Numerical methods such as Finite Difference (FD) modelling and Spectral Element Methods (SEM) are the most popular techniques for simulating complex media, but tasks their computational cost prohibitively expensive. In this work we present two types deep neural networks fast alternatives horizontally layered faulted 2D acoustic media. contrast to classical both able simulate response at multiple...

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a network approximate the solution PDE and incorporate residual as well conditions into its loss function when training it. This provides simple mesh-free relating PDEs. However, limitation their lack accuracy efficiency with larger domains more complex, multi-scale solutions. In recent approach, finite basis...

Population balance equation (PBE) models have potential to automate many engineering processes with far-reaching implications. In the pharmaceutical sector, crystallization model-based design can contribute shortening excessive drug development timelines. Even so, two major barriers, typical of most transport equations, not just PBEs, limited this potential. Notably, time taken compute a solution these representative accuracy is frequently limiting. Likewise, model construction process often...

Lunar exploration missions require detailed and accurate planning to ensure their safety. Remote sensing data, such as optical satellite imagery acquired by lunar orbiters, are key for the identification of future landing mission sites. Here robot- astronaut-scale obstacles most relevant resolve; however, spatial resolution available image data is often insufficient, particularly in poorly illuminated polar regions moon, leading uncertainty. This work shows how a novel single-image...

We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models large data, which the access to data is restricted some way. Our main result if regularizer's effect does not become negligible as norm of hypothesis scales, then a uniform sample modest size with high probability coreset. In case function either logistic regression or soft-margin support vector machines, regularizer one common...

Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve with high frequency and/or multi-scale solutions. Finite basis physics-informed (FBPINNs) improve the performance of PINNs in this regime by combining them an overlapping domain decomposition approach. In work, FBPINNs extended adding multiple levels decompositions their solution ansatz, inspired classical multilevel Schwarz methods (DDMs)....