arXiv research

Bayesian Neural Networks improve geophysical model ensembles with reduced uncertainty.

Kernel methods improve geophysical forecasting accuracy and efficiency.

SDA method reduces memory and time for assimilating noisy geophysical data.

Physics-constrained deep learning predicts geophysical dynamics with boundedness.

Deep models memorize training data in geophysical inversion, leading to biased posterior distributions.

The paper calibrates geophysical predictions using marginal distributions and machine learning.

This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling of stationary time series with consistent properties facilitates prediction with…

Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties…

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 of which might lead to undesirable results. To overcome this issue, we have deve…

Neural architecture improves geophysical data assimilation with uncertainty quantification.

Physics-consistent method improves seismic inversion accuracy.

Improved variational inference for geophysical inverse problems with data correction.

Method improves clarity in forecasting spatio-temporal data.

Study uses neural fields to improve geophysical inversions by reducing artifacts.

Geostatistical learning faces unique challenges due to spatial correlation and covariate shifts.

Automated quality control for seismic data reduces human labor and time.

A fundamental problem in geophysical modeling is related to the identification and approximation of causal structures among physical processes. However, resolving the bidirectional mappings between physical parameters and model state variables (i.e., solving the forward and inverse problems) is challenging, especially …

TSCoNet forecasts correlated geophysical fields with uncertainty estimates.

Order patterns and permutation entropy have become useful tools for studying biomedical, geophysical or climate time series. Here we study day-to-day market data, and Brownian motion which is a good model for their order patterns. A crucial point is that for small lags (1 up to 6 days), pattern frequencies in financial…

The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find th…

Gaussian Processes improve geoscience data analysis.

We analyze the inverse problem, originally formulated by Dix in geophysics, of reconstructing the wave speed inside a domain from boundary measurements associated with the single scattering of seismic waves. We consider a domain $\tilde M$ with a varying and possibly anisotropic wave speed which we model as a Riemannia…

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference fro…

Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on Riemannian or Lorentzian manifolds and includes an investigation of the existen…

The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and more appealing to benefit from available large-scale observation and simulation dat…

Empirical mode modeling improves state-space analysis of noisy data.

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and because we can only get few measurements. This setting is common in geophysical ima…

Deep Learning is gaining traction with geophysics community to understand subsurface structures, such as fault detection or salt body in seismic data. This study describes using deep learning method for iceberg or ship recognition with synthetic aperture radar (SAR) data. Drifting icebergs pose a potential threat to ac…

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extr…

We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds …

Data scientists guide to streamflow prediction and flood forecasting.

Fractal Flow enhances normalizing flows with interpretable latent space and hierarchical modeling.

This paper tackles learning functions on manifolds using parallel distributed learning.

One of the most important applications of seismic reflection is the hydrocarbon exploration which is closely related to salt deposits analysis. This problem is very important even nowadays due to it's non-linear nature. Taking into account the recent developments in deep learning networks TGS-NOPEC Geophysical Company …

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal variability. The data sets associated with many of these processes are increasing …

CGAN fails to improve deterministic sequence predictions, revealing a theoretical limitation.

We discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. …

Model infers mineral locations from geospatial data, improving predictions with auxiliary data.

How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysi…

We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using Kullback-Leibler divergence we evaluate the best model out from four biparametric mod…

In the geophysical field, seismic noise attenuation has been considered as a critical and long-standing problem, especially for the pre-stack data processing. Here, we propose a model to leverage the deep-learning model for this task. Rather than directly applying an existing de-noising model from ordinary images to th…

Review of diffusion models for SBI in non-ideal data scenarios.

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is mo…

We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap …

In this paper, we compute the sectional curvature of the quantomorphism group $\mathcal{D}_q(M)$ whose geodesic equation is the quasi-geostrophic (QG) equation in geophysics and oceanography, for flows with a stream function depending on only one variable. Using this explicit formula, we will also derive a criterion fo…

Consider a broken geodesics $α([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for every broken geodesic $α([0,l])$ starting at and ending to the boundary $\partial M$…

Geometric integrator preserves coadjoint orbits in dissipative systems.