Bayesian inversion of coupled radiative and heat transfer models for asteroid regoliths and lakes

Schiassi, Enrico; Furfaro, Roberto; Mostacci, Domiziano

doi:10.1080/10420150.2016.1253091

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…Hence the output of the inverse modeling will be the probability distribution for each of those quantities. With this approach, the degree of uncertainty of the water component concentrations actual values is included in their probability distributions (Schiassi et al, 2016). Importantly, GLAM BioLith-RT code is developed and deployed in a modular source format.…”

Section: Figurementioning

confidence: 99%

“…However, as we deal with probability distributions, along with the mean, we will have the estimate of the variance which is a valuable piece of extra information to evaluate our trust in the retrieved estimations (Theodoridis, 2015). Moreover, as stated in Schiassi et al (2016) and Kolehmainen (2013), another advantage of the Bayesian approach is that ill-posedness are removed by using prior information about the solutions. Since all variables are considered random, the randomness reflects the uncertainty about their true values; and the degree of uncertainty is intrinsically coded in the probability distribution of these variables.…”

Section: Bayesian Inversion Vs Standard Constrained Optimizationmentioning

confidence: 99%

“…According to Kolehmainen (2013) the degree of uncertainty is embedded in these densities and the random nature of these variables reflects the uncertainty on their true values. This distribution is called posterior and is the combination of the prior distribution, for the quantities to estimate, with the observed data via the Bayes' rule (Rogers and Girolami, 2003;Schiassi et al, 2016):…”

Section: Bayesian Inversionmentioning

confidence: 99%

“…where, in accordance with the notations in Schiassi et al (2016), m are the observed data, x are the parameters to retrieve, Ŵ(m|x) is the likelihood function (i.e., the probability distribution for the observed data given the parameters to retrieve), π pr (x) is the prior distribution for the parameters to fit, and π(m) is the marginal likelihood (normalization constant). The posterior distribution is then used to compute expectation in the form: In the cases of interest quantities such as 19 are impossible to evaluate analytically.…”

Section: Bayesian Inversionmentioning

confidence: 99%

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GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

et al. 2019

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A new open-source software tool, called GLAM BioLith-RT (Glacier Lakes Assisted Melting Biological Lithological Radiative Transfer), has been developed for modeling of Radiative Transfer (RT) in water bodies containing suspended lithic particles, phytoplankton, dissolved salts, and colored dissolved organic matter. Although our objective is an application to glacial lakes of High Mountain Asia, the model has potential application for the study of seawater, organic-rich lakes, rivers, etc. The tool is built on a solid foundation of an existing published open-source code called WASI, which has been reviewed and augmented with new capabilities, notably the addition of a suspended lithic particle grain size parameterization. GLAM BioLith-RT operates in both a forward modeling and inverse modeling mode. The forward mode is specifically designed to compute the reflectance spectra of glacier lakes from inherent optical water properties. Conversely, in the inverse mode, measured spectral reflectance is employed with other inputs to derive best fitting water component properties (e.g., suspended particles concentration). The inverse modeling includes Bayesian inversion of the output which is a significant advance over the existing software. We have tested the code for sensitivity to noise, and uncertainties in input parameters. The model succeeds in nearly reproducing the hyperspectral reflectance of some glacial lakes in Nepal as observed by the EO-1 Hyperion hyperspectral imager. The inverse modeling approach, when supported up by validated forward modeling, offers a means for remote sensing characterization of suspended sediment load in glacial lakes and rivers and hence, use of suspended sediment as a proxy for glacial activity; and many other potential applications in other thematic areas.

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Section: Figurementioning

confidence: 99%

Section: Bayesian Inversion Vs Standard Constrained Optimizationmentioning

confidence: 99%

Section: Bayesian Inversionmentioning

confidence: 99%

Section: Bayesian Inversionmentioning

confidence: 99%

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GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

et al. 2019

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“…This method aims to solve forward problems and inverse problems (data-driven parameters discovery) involving DEs in different perturbation scenarios. A typical field where solving inverse problems is of interest is remote sensing [26][27][28][29]. For instance, in Reference [30], the authors combine radiative and heat transfer equations to create a set of parametric DEs.…”

Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

et al. 2021

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In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional Connections (X-TFC), for data-physics-driven parameters’ discovery of problems modeled via Ordinary Differential Equations (ODEs). The proposed method merges the standard PINNs with a functional interpolation technique named Theory of Functional Connections (TFC). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS). The results show the low computational times, the high accuracy, and effectiveness of the X-TFC method in performing data-driven parameters’ discovery systems modeled via parametric ODEs using unperturbed and perturbed data.

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Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations

et al. 2021

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Bayesian inversion of coupled radiative and heat transfer models for asteroid regoliths and lakes

Cited by 5 publications

References 3 publications

GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations

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