arXiv subjects

Velimir V. Vesselinov

Publications and source records attributed to Velimir V. Vesselinov.

16 recordsLinked to original sources

arXiv2022

GeoThermalCloud: Machine Learning for Geothermal Resource Exploration

This paper presents a novel ML-based methodology for geothermal exploration towards PFA applications. Our methodology is provided through our open-source ML framework, GeoThermalCloud \url{https://github.com/SmartTensors/GeoThermalCloud.jl}. The GeoThermalCloud uses a series of unsupervised, supervised, and physics-informed ML methods available in SmartTensors AI platform \url{https://github.com/SmartTensors}. Here, the presented analyses are performed using our unsupervised ML algorithm called NMF$k$, which is available in the SmartTensors AI platform. Our ML algorithm facilitates the discovery of new phenomena, hidden patterns, and mechanisms that helps us to make informed decisions. Moreover, the GeoThermalCloud enhances the collected PFA data and discovers signatures representative of geothermal resources. Through GeoThermalCloud, we could identify hidden patterns in the geothermal field data needed to discover blind systems efficiently. Crucial geothermal signatures often overlooked in traditional PFA are extracted using the GeoThermalCloud and analyzed by the subject matter experts to provide ML-enhanced PFA, which is informative for efficient exploration. We applied our ML methodology to various open-source geothermal datasets within the U.S. (some of these are collected by past PFA work). The results provide valuable insights into resource types within those regions. This ML-enhanced workflow makes the GeoThermalCloud attractive for the geothermal community to improve existing datasets and extract valuable information often unnoticed during geothermal exploration.

cs.LG↗

arXiv2022

Nonequilibrium Statistical Mechanics and Optimal Prediction of Partially-Observed Complex Systems

Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g., hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system's future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel Maximum Entropy and Maximum Caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori-Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining implicit and explicit aspects.

cond-mat.stat-mech↗

arXiv2019

Learning to regularize with a variational autoencoder for hydrologic inverse analysis

Inverse problems often involve matching observational data using a physical model that takes a large number of parameters as input. These problems tend to be under-constrained and require regularization to impose additional structure on the solution in parameter space. A central difficulty in regularization is turning a complex conceptual model of this additional structure into a functional mathematical form to be used in the inverse analysis. In this work we propose a method of regularization involving a machine learning technique known as a variational autoencoder (VAE). The VAE is trained to map a low-dimensional set of latent variables with a simple structure to the high-dimensional parameter space that has a complex structure. We train a VAE on unconditioned realizations of the parameters for a hydrological inverse problem. These unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any forward runs of the physical model, thus making the computational cost of generating the training data minimal. The central benefit of this approach is that regularization is then performed on the latent variables from the VAE, which can be regularized simply. A second benefit of this approach is that the VAE reduces the number of variables in the optimization problem, thus making gradient-based optimization more computationally efficient when adjoint methods are unavailable. After performing regularization and optimization on the latent variables, the VAE then decodes the problem back to the original parameter space. Our approach constitutes a novel framework for regularization and optimization, readily applicable to a wide range of inverse problems. We call the approach RegAE.

physics.comp-ph↗

arXiv2018

Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, in this paper, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.

cs.LG↗

arXiv2018

Identification of release sources in advection-diffusion system by machine learning combined with Green function inverse method

The identification of sources of advection-diffusion transport is based usually on solving complex ill-posed inverse models against the available state- variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influences of the original sources. Importantly, the number of these original release sources is typically unknown, which hinders reliability of the classical inverse-model analyses. To address this challenge, we present here a novel hybrid method for identification of the unknown number of release sources. Our hybrid method, called HNMF, couples unsupervised learning based on Nonnegative Matrix Factorization (NMF) and inverse-analysis Green functions method. HNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green function of advection-diffusion equation to identify their characteristics. In the paper, we introduce the method and demonstrate that it is capable of identifying the advection velocity and dispersivity of the medium as well as the unknown number, locations, and properties of various sets of synthetic release sources with different space and time dependencies, based only on the recorded data. HNMF can be applied directly to any problem controlled by a partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations.

cs.LG↗

arXiv2018

Unsupervised Phase Mapping of X-ray Diffraction Data by Nonnegative Matrix Factorization Integrated with Custom Clustering

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new method for pattern analysis and phase extraction of XRD datasets. The method expands the Nonnegative Matrix Factorization method, which has been used previously to analyze such datasets, by combining it with custom clustering and cross-correlation algorithms. This new method is capable of robust determination of the number of basis patterns present in the data which, in turn, enables straightforward identification of any possible peak-shifted patterns. Peak-shifting arises due to continuous change in the lattice constants as a function of composition, and is ubiquitous in XRD datasets from composition spread libraries. Successful identification of the peak-shifted patterns allows proper quantification and classification of the basis XRD patterns, which is necessary in order to decipher the contribution of each unique single-phase structure to the multi-phase regions. The process can be utilized to determine accurately the compositional phase diagram of a system under study. The presented method is applied to one synthetic and one experimental dataset, and demonstrates robust accuracy and identification abilities.

cond-mat.mtrl-sci↗

arXiv2017

Inferring subsurface heterogeneity from push-drift tracer tests

We consider the late-time tailing in a tracer test performed with a push-drift methodology (i.e., quasi-radial injection followed by drift under natural gradient). Numerical simulations of such tests are performed on 1000 multi-Gaussian 2D log-hydraulic conductivity field realizations of varying heterogeneity, each under eight distinct mean flow directions. The ensemble pdfs of solute return times are found to exhibit power law tails for each considered variance of the log-hydraulic conductivity field, $σ^2_{\ln K}$. The tail exponent is found to relate straightforwardly to $σ^2_{\ln K}$ and, within the parameter space we explored, to be independent of push-phase pumping rate and pumping duration. We conjecture that individual push-drift tracer tests in wells with screened intervals much greater than the vertical correlation length of the aquifer will exhibit quasi-ergodicity and that their tail exponent may be used to infer $σ^2_{\ln K}$. We calibrate a predictive relationship of this sort from our Monte Carlo study, and apply it to data from a push-drift test performed at a site of approximately known heterogeneity---closely matching the existing best estimate of heterogeneity.

physics.geo-ph↗

arXiv2017

Nonnegative/binary matrix factorization with a D-Wave quantum annealer

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images.

cs.LG↗

arXiv2017

Local equilibrium and retardation revisited

In modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption. Assuming local equilibrium (LE), Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of mass transfer, applicable even in the case of arbitrarily fast mass transfer. First, we resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that LE constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. Second, we present a numerical particle tracking study of transport in a heterogeneous aquifer subject to first-order MIMT. Transport is modeled (a) exactly, and then (b) approximated with the retarded ADE. Strikingly different results are obtained, even though quasi-LE is maintained at all times by the exact MIMT simulation. We thus observe that use of the phrase local equilibrium assumption to refer to ADE validity is not correct. We highlight that solute remobilization rate is the true control on retarded ADE validity, and note that classic "local equilibrium assumption" (i.e., ADE validity) criteria actually test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium.

physics.flu-dyn↗

arXiv2017

Characterizing the impact of model error in hydrogeologic time series recovery inverse problems

Hydrogeologic models are commonly over-smoothed relative to reality, owing to the difficulty of obtaining accurate high-resolution information about the subsurface. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased "observation noise" term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. Here, model error is considered for a hydrogeologically important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of systematic model error on time series recovery for both well-determined and over-determined inverse problems. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. A possible diagnostic criterion for blind transfer function characterization is also uncovered.

math.SP↗

arXiv2017

CHROTRAN: A mathematical and computational model for in situ heavy metal remediation in heterogeneous aquifers

Groundwater contamination by heavy metals is a critical environmental problem for which in situ remediation is frequently the only viable treatment option. For such interventions, a three-dimensional reactive transport model of relevant biogeochemical processes is invaluable. To this end, we developed a model, CHROTRAN, for in situ treatment, which includes full dynamics for five species: a heavy metal to be remediated, an electron donor, biomass, a nontoxic conservative bio-inhibitor, and a biocide. Direct abiotic reduction by donor-metal interaction as well as donor-driven biomass growth and bio-reduction are modeled, along with crucial processes such as donor sorption, bio-fouling and biomass death. Our software implementation handles heterogeneous flow fields, arbitrarily many chemical species and amendment injection points, and features full coupling between flow and reactive transport. We describe installation and usage and present two example simulations demonstrating its unique capabilities. One simulation suggests an unorthodox approach to remediation of Cr(VI) contamination.

q-bio.OT↗

arXiv2014

Robust decision analysis for environmental management of groundwater contamination sites

In contrast to many other engineering fields, the uncertainties in subsurface processes (e.g., fluid flow and contaminant transport in aquifers) and their parameters are notoriously difficult to observe, measure, and characterize. This causes severe uncertainties that need to be addressed in any decision analysis related to optimal management and remediation of groundwater contamination sites. Furthermore, decision analyses typically rely heavily on complex data analyses and/or model predictions, which are often poorly constrained as well. Recently, we have developed a model-driven decision-support framework (called MADS; http://mads.lanl.gov) for the management and remediation of subsurface contamination sites in which severe uncertainties and complex physics-based models are coupled to perform scientifically defensible decision analyses. The decision analyses are based on Information Gap Decision Theory (IGDT). We demonstrate the MADS capabilities by solving a decision problem related to optimal monitoring network design.

stat.AP↗

arXiv2011

Adaptive hybrid optimization strategy for calibration and parameter estimation of physical models

A new adaptive hybrid optimization strategy, entitled squads, is proposed for complex inverse analysis of computationally intensive physical models. The new strategy is designed to be computationally efficient and robust in identification of the global optimum (e.g. maximum or minimum value of an objective function). It integrates a global Adaptive Particle Swarm Optimization (APSO) strategy with a local Levenberg-Marquardt (LM) optimization strategy using adaptive rules based on runtime performance. The global strategy optimizes the location of a set of solutions (particles) in the parameter space. The LM strategy is applied only to a subset of the particles at different stages of the optimization based on the adaptive rules. After the LM adjustment of the subset of particle positions, the updated particles are returned to the APSO strategy. The advantages of coupling APSO and LM in the manner implemented in squads is demonstrated by comparisons of squads performance against Levenberg-Marquardt (LM), Particle Swarm Optimization (PSO), Adaptive Particle Swarm Optimization (APSO; the TRIBES strategy), and an existing hybrid optimization strategy (hPSO). All the strategies are tested on 2D, 5D and 10D Rosenbrock and Griewank polynomial test functions and a synthetic hydrogeologic application to identify the source of a contaminant plume in an aquifer. Tests are performed using a series of runs with random initial guesses for the estimated (function/model) parameters. Squads is observed to have the best performance when both robustness and efficiency are taken into consideration than the other strategies for all test functions and the hydrogeologic application.

physics.geo-ph↗

arXiv2011

Unified Analytical Solution for Radial Flow to a Well in a Confined Aquifer

Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper [1967]; Hantush [1964] when the pumping well has no wellbore storage; Theis [1935] when both conditions are fulfilled and Yang et.al. [2006] when the pumping well is partially penetrating, has finite radius but lacks storage. We use our solution to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.

math-ph↗

arXiv2011

Contaminant remediation decision analysis using information gap theory

Decision making under severe lack of information is a ubiquitous situation in nearly every applied field of engineering, policy, and science. A severe lack of information precludes our ability to determine a frequency of occurrence of events or conditions that impact the decision; therefore, decision uncertainties due to a severe lack of information cannot be characterized probabilistically. To circumvent this problem, information gap (info-gap) theory has been developed to explicitly recognize and quantify the implications of information gaps in decision making. This paper presents a decision analysis based on info-gap theory developed for a contaminant remediation scenario. The analysis provides decision support in determining the fraction of contaminant mass to remove from the environment in the presence of a lack of information related to the contaminant mass flux into an aquifer. An info-gap uncertainty model is developed to characterize uncertainty due to a lack of information concerning the contaminant flux. The info-gap uncertainty model groups nested, convex sets of functions defining contaminant flux over time based on their level of deviation from a nominal contaminant flux. The nominal contaminant flux defines a reasonable contaminant flux over time based on existing information. A robustness function is derived to quantify the maximum level of deviation from nominal that still ensures compliance for each decision. An opportuneness function is derived to characterize the possibility of meeting a desired contaminant concentration level. The decision analysis evaluates how the robustness and opportuneness change as a function of time since remediation and as a function of the fraction of contaminant mass removed.

physics.geo-ph↗

arXiv2011

Accounting for the influence of aquifer heterogeneity on spatial propagation of pumping drawdown

It has been previously observed that during a pumping test in heterogeneous media, drawdown data from different time periods collected at a single location produce different estimates of aquifer properties and that Theis type-curve inferences are more variable than late-time Cooper-Jacob inferences. In order to obtain estimates of aquifer properties from highly transient drawdown data using the Theis solution, it is necessary to account for this behavior. We present an approach that utilizes an exponential functional form to represent Theis parameter behavior resulting from the spatial propagation of a cone of depression. This approach allows the use of transient data consisting of early-time drawdown data to obtain late-time convergent Theis parameters consistent with Cooper-Jacob method inferences. We demonstrate the approach on a multi-year dataset consisting of multi-well transient water-level observations due to transient multi-well water-supply pumping. Based on previous research, transmissivities associated with each of the pumping wells are required to converge to a single value, while storativities are allowed to converge to distinct values.

physics.geo-ph↗