arXiv subjects

Juan M. Restrepo

Publications and source records attributed to Juan M. Restrepo.

At least 19 recordsLinked to original sources

arXiv2024

A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems -waves-, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

math.DS↗

arXiv2024

Estimating an Executive Summary of a Time Series: The Tendency

In this paper we revisit the problem of decomposing a signal into a tendency and a residual. The tendency describes an executive summary of a signal that encapsulates its notable characteristics while disregarding seemingly random, less interesting aspects. Building upon the Intrinsic Time Decomposition (ITD) and information-theoretical analysis, we introduce two alternative procedures for selecting the tendency from the ITD baselines. The first is based on the maximum extrema prominence, namely the maximum difference between extrema within each baseline. Specifically this method selects the tendency as the baseline from which an ITD step would produce the largest decline of the maximum prominence. The second method uses the rotations from the ITD and selects the tendency as the last baseline for which the associated rotation is statistically stationary. We delve into a comparative analysis of the information content and interpretability of the tendencies obtained by our proposed methods and those obtained through conventional low-pass filtering schemes, particularly the Hodrik-Prescott (HP) filter. Our findings underscore a fundamental distinction in the nature and interpretability of these tendencies, highlighting their context-dependent utility with emphasis in multi-scale signals. Through a series of real-world applications, we demonstrate the computational robustness and practical utility of our proposed tendencies, emphasizing their adaptability and relevance in diverse time series contexts.

eess.SP↗

arXiv2023

Probabilistic Measures for Biological Adaptation and Resilience

This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from non-equilibrium statistical mechanics, we propose a measure termed `ecological resilience through adaptation,' specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems, and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

q-bio.QM↗

arXiv2022

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. This report summarizes the outcomes of that workshop, "Randomized Algorithms for Scientific Computing (RASC)," held virtually across four days in December 2020 and January 2021.

cs.AI↗

arXiv2022

Uncertainty in Climate Science: Not Cause for Inaction

Using observational data and an elementary rigorous statistical fact it is easily shown that the distribution of Earth's climate is non-stationary. Examination of records of hundreds of local Industrial Era temperature histories in the Northern Hemisphere were used to show this fact. Statistically, the mean of the ensemble has been rising during the Industrial Era. All of this confirms what climate scientists already know. The issue of predictions under uncertainties was tackled as well: a simple balance model was tuned to track an ensemble of climate records. Stochastic parametrizations were created to capture natural and anthropogenic CO2 forcings. The resulting stochastic model was then tested against historical data and then used to make future predictions. This exercise confirmed as well climate science attribution to significant global warming during the Industrial Era to anthropogenic activities. The variability of the model due to uncertainties is simply not large enough to obfuscate a clear rise in the mean temperature in the Industrial Era. Further, even if the variance of the natural CO2 contribution is greatly increased artificially (in the model), the fluctuations cannot account for the current change in the historical mean. These outcomes weaken the factual validity of the US administration, 2016-2020, claims that there are too many uncertainties in climate and climate science to make climate predictions, and further that contemporary reports of floods, extreme weather, even a rising global mean temperature are simply manifestations of a climate that always fluctuates within a nature-derived statistical distribution.

physics.ao-ph↗

arXiv2021

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high quality balanced mesh is produced.

math.NA↗

arXiv2021

Maximal Poisson-disk Sampling for Variable Resolution Conforming Delaunay Mesh Generation: Applications for Three-Dimensional Discrete Fracture Networks and the Surrounding Volume

We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2- and 3-dimensions in linear run time. The effectiveness of the algorithm is demonstrated by generating an unstructured 3D mesh on a discrete fracture network (DFN). Even though Poisson-disk sampling methods do not provide triangulation quality bounds in more than two-dimensions, we found that low quality tetrahedra are infrequent enough and could be successfully removed to obtain high quality balanced three-dimensional meshes with topologically acceptable tetrahedra.

math.NA↗

arXiv2021

Homotopy Sampling, with an Application to Particle Filters

We propose a homotopy sampling procedure, loosely based on importance sampling. Starting from a known probability distribution, the homotopy procedure generates the unknown normalization of a target distribution. In the context of stationary distributions that are associated with physical systems the method is an alternative way to estimate an unknown microcanonical ensemble. The process is iterative and also generates samples from the target distribution. In practice, the homotopy procedure does not circumvent using sample averages in the estimation of the normalization constant. The error in the procedure depends on the errors incurred in sample averaging and the number of stages used in the computational implementation of the process. However, we show that it is possible to exchange the number of homotopy stages and the total number of samples needed at each stage in order to enhance the computational efficiency of the implemented algorithm. Estimates of the error as a function of stages and sample averages are derived. These could guide computational efficiency decisions on how the calculation would be mapped to a given computer architecture. Consideration is given to how the procedure can be adapted to Bayesian estimation problems, both stationary and non-stationary. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique known as particle filtering. It is shown that a modification of the particle filter framework to include the homotopy process can improve the computational robustness of particle filters. The homotopy process can ameliorate particle filter collapse, a common challenge to using particle filters when the sample dimension is small compared with the state space dimensions.

stat.CO↗

arXiv2020

Gradient Sensing via Cell Communication

Experimental evidence lends support to the conjecture that the ability of chains of cells to sense the gradient of an external chemical concentration could rely on cell-to-cell communication. This is the basis for the gradient sensing nature of a specific model type of the Local Excitation, Global Inhibition (LEGI) principle, wherein the strength of the external chemical field is sensed through a comparison between a local exciting species and a global inhibitor that is shared via intra-cellular reactions in the cell chain. In this study we generalize the nearest neighbor communication mechanism in the above-mentioned LEGI model in order to explore how the chemical sensing characteristics depend on the parameterization of the communication itself, cell size, and the radius of influence of neighboring cells. It was found that the radius of influence was less important than the approximating model for communication. Higher order approximations to the communication mechanism were better able to sense an external gradient. However, an analysis of the signal to noise ratio established that higher order models for communication were more prone to noise and thus have a lower signal to noise ratio. The generalization as well as the tools used in the analysis of the dynamics can be extended to more heterogeneous networks and can thus prove useful in using models and observations in the process of understanding chemical gradient via LEGI models with a communication component.

q-bio.QM↗

arXiv2018

Transport due to Transient Progressive Waves

We describe and analyze the mean transport due to transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced air-water two-phase Navier Stokes solver. The analysis is done in the Lagrangian frame. We show that the transport generated by these waves is significantly larger than the transport generated by steady waves. The numerically generated parcel paths suggest a model for the transport that is primarily driven by an irrotational approximation of the velocity. Wave breaking is shown to increase the variability in the transport. Breaking is accounted for in the transport model via an additive stochastic velocity term.

physics.flu-dyn↗

arXiv2018

Rain Calms the Sea - The Impact of Entrained Air

We propose a mechanism for the damping of short ocean gravity waves during rainstorms associated with the injection of air bubbles by rain drops. The mechanism is proposed as one of the possible explanations that ascribe to rain a calming effect on ocean surface waves. A model is developed that shows how wave attenuation increases with the presence of air bubbles in the upper reaches of the ocean. The model makes predictions of the effective wave dissipation coefficient, as a function of the volumetric ratio of air to water, as well as to the rainfall rate. The model predicts dissipation rates that are in line with experimental estimates of the effective wave damping rate.

physics.flu-dyn↗

arXiv2017

Dynamic Likelihood Filter

A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically update the likelihood with the aim of making better use of low uncertainty sparse observations. The filter is applied to a problem with linear dynamics and Gaussian statistics, and compared to the exact estimate, a model outcome, and the Kalman filter estimate. Its estimates are shown to be superior to the model outcomes and the Kalman estimate, when the observation system is sparse. The added computational expense of the method is linear in the number of observations and thus computationally efficient, suggesting that the method is practical even if the space dimensions of the physical problem are large.

math.DS↗

arXiv2017

Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport

We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and lumping them together would compromise the accuracy of the resulting model. Without observational or computational constraints, it is thus not possible to quantitatively predict oil spills based upon partial field observations of surface and/or sub-surface oil. The primary challenge in capturing the mass exchange is that the principal mechanisms are on the microscale. This is a serious barrier to developing practical models for oil spills that are capable of addressing questions regarding the fate of oil at the large spatio-temporal scales, as demanded by environmental questions. We use upscaling to propose an environmental-scale model which incorporates the mass exchange between surface and subsurface oil due to oil droplet dynamics, buoyancy effects, and sea surface and subsurface mechanics. While the mass exchange mechanism detailed here is generally applicable to oil transport models, it addresses the modeling needs of a particular to an oil spill model [1]. This transport model is designed to capture oil spills at very large spatio-temporal scales. It accomplishes this goal by specializing to shallow-water environments, in which depth averaging is a perfectly good approximation for the flow, while at the same time retaining mass conservation of oil over the whole oceanic domain.

physics.ao-ph↗

arXiv2017

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.

cond-mat.stat-mech↗

arXiv2016

Stochastic Longshore Current Dynamics

We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call {\em consistency of sensitivity}. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation {\em that were not used} in tuning the model.

physics.data-an↗

arXiv2016

Displacement Data Assimilation

We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information important. While the displacement transformation is not tied to any particular assimilation scheme, here we implement it within an ensemble Kalman Filter and demonstrate its effectiveness in tracking stochastically perturbed vortices.

physics.data-an↗

arXiv2014

Nearshore sticky waters

Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters.

physics.flu-dyn↗

arXiv2014

Defining a Trend for a Time Series Which Makes Use of the Intrinsic Time-Scale Decomposition

We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the {\it tendency} of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the Intrinsic Time-Scale Decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.

physics.data-an↗