Related papers: Efficient big data assimilation through sparse rep…
Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of…
Nonlinear least squares data-fitting driven by physical process simulation is a classic and widely successful technique for the solution of inverse problems in science and engineering. Known as "Full Waveform Inversion" in application to…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
Seismic images obtained by stacking or migration are usually characterized as low signal-to-noise ratio (SNR), low dominant frequency and sparse sampling both in depth (or time) and offset dimensions. For improving the resolution of seismic…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
The {\em wavelet tree} is a flexible data structure that permits representing sequences $S[1,n]$ of symbols over an alphabet of size $\sigma$, within compressed space and supporting a wide range of operations on $S$. When $\sigma$ is…
We propose a novel deep learning framework, named SYMHnet, which employs a graph neural network and a bidirectional long short-term memory network to cooperatively learn patterns from solar wind and interplanetary magnetic field parameters…
Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack…
The need for accurate and fast scale-resolving simulations of fluid flows, where turbulent dispersion is a crucial physical feature, is evident. Large-eddy simulations (LES) are computationally more affordable than direct numerical…
The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used.…
Seismic noise with an amplitude higher than that of the sought signal is a challenge for detection. Several techniques have been developed to suppress the ambient noise and to reduce the detection threshold in order to find signals with the…
In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression,…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are…
Sparse Autoencoders (SAEs) have emerged as a predominant tool in mechanistic interpretability, aiming to identify interpretable monosemantic features. However, how does sparse encoding organize the representations of activation vector from…
In exploration seismology, seismic inversion refers to the process of inferring physical properties of the subsurface from seismic data. Knowledge of physical properties can prove helpful in identifying key structures in the subsurface for…
Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…