Developing open-source tools for reproducible inverse problems: the PyLops journey

2021 ◽  
Author(s):  
Matteo Ravasi ◽  
Carlos Alberto da Costa Filho ◽  
Ivan Vasconcelos ◽  
David Vargas
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Mathematical Formulation ◽  
Optimization Methods ◽  
Linear Operators ◽  
Gravity Potential ◽  
Nonlinear Inversion ◽  
Unified Framework ◽  
Computationally Intensive ◽  
High Level

<p>Inverse problems lie at the core of many geophysical algorithms, from earthquake and exploration seismology, all the way to electromagnetics and gravity potential methods.</p><p>In 2018, we open-sourced PyLops, a Python-based framework for large-scale inverse problems. By leveraging the concept of matrix-free linear operators – together with the efficiency of numerical libraries such as NumPy, SciPy, and Numba – PyLops solves computationally intensive inverse problems with high-level code that is highly readable and resembles the underlying mathematical formulation. While initially aimed at researchers, its parsimonious software design choices, large test suite, and thorough documentation render PyLops a reliable and scalable software package easy to run both locally and in the cloud.</p><p>Since its initial release, PyLops has incorporated several advancements in scientific computing leading to the creation of an entire ecosystem of tools: operators can now run on GPUs via CuPy, scale to distributed computing through Dask, and be seamlessly integrated into PyTorch’s autograd to facilitate research in machine-learning-aided inverse problems. Moreover, PyLops contains a large variety of inverse solvers including least-squares, sparsity-promoting algorithms, and proximal solvers highly-suited to convex, possibly nonsmooth problems. PyLops also contains sparsifying transforms (e.g., wavelets, curvelets, seislets) which can be used in conjunction with the solvers. By offering a diverse set of tools for inverse problems under one unified framework, it expedites the use of state-of-the-art optimization methods and compressive sensing techniques in the geoscience domain.</p><p>Beyond our initial expectations, the framework is currently used to solve problems beyond geoscience, including astrophysics and medical imaging. Likewise, it has inspired the development of the occamypy framework for nonlinear inversion in geophysics. In this talk, we share our experience in building such an ecosystem and offer further insights into the needs and interests of the EGU community to help guide future development as well as achieve wider adoption.</p>

scholarly journals Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 174-187 ◽  
Author(s):  
William Rodi ◽  
Randall L. Mackie
Keyword(s):  
Inverse Problems ◽  
Objective Function ◽  
Complete Solution ◽  
Model Space ◽  
Conjugate Gradients ◽  
Nonlinear Inversion ◽  
Spatial Derivatives ◽  
Computationally Intensive ◽  
Derivatives Of ◽  
Special Case

We investigate a new algorithm for computing regularized solutions of the 2-D magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such “minimum‐structure” models: the Gauss‐Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie‐Madden) are more efficient than the Gauss‐Newton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients‐based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss‐Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie‐Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie‐Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

scholarly journals An open-source framework for the implementation of large-scale integral operators with flexible, modern HPC solutions - Enabling 3D Marchenko imaging by least squares inversion

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Matteo Ravasi ◽  
Ivan Vasconcelos
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Distributed Storage ◽  
Integral Operators ◽  
Linear Operators ◽  
Spatial Direction ◽  
Full Dataset ◽  
Systems Of Integral Equations ◽  
Gradient Based ◽  
High Level

Numerical integral operators of convolution type form the basis of most wave-equation-based methods for processing and imaging of seismic data. As several of these methods require the solution of an inverse problem, multiple forward and adjoint passes of the modeling operator are generally required to converge to a satisfactory solution. This work highlights the memory requirements and computational challenges that arise when implementing such operators on 3D seismic datasets and their usage for solving large systems of integral equations. A Python framework is presented that leverages libraries for distributed storage and computing, and provides a high-level symbolic representation of linear operators. A driving goal for our work is not only to offer a widely deployable, ready-to-use high-performance computing (HPC) framework, but to demonstrate that it enables addressing research questions that are otherwise difficult to tackle. To this end, the first example of 3D full-wavefield target-oriented imaging, which comprises of two subsequent steps of seismic redatuming, is presented. The redatumed fields are estimated by means of gradient-based inversion using the full dataset as well as spatially decimated versions of the dataset as a way to investi-gate the robustness of both inverse problems to spatial aliasing in the input dataset. Our numerical example shows that when one spatial direction is finely sampled, satisfactory redatuming and imaging can be accomplished also when the sampling in other direction is coarser than a quarter of the dominant wavelength. While aliasing introduces noise in the redatumed fields, they are less sensitive to well-known spurious artefacts compared to cheaper, adjoint-based redatuming techniques. These observations are shown to hold for a relatively simple geologic structure, and while further testing is needed for more complex scenarios, we expect them to be generally valid while possibly breaking down for extreme cases

Social inequality in the evolution of human societies

2019 ◽  
pp. 98-120
Author(s):  
Georgi Derluguian
Keyword(s):  
Social Inequality ◽  
Large Scale ◽  
Human Beings ◽  
Mass Violence ◽  
Public And Private ◽  
Tangible Assets ◽  
Transition To Agriculture ◽  
New Institutions ◽  
High Level ◽  
Political Economic

The author develops ideas about the origin of social inequality during the evolution of human societies and reflects on the possibilities of its overcoming. What makes human beings different from other primates is a high level of egalitarianism and altruism, which contributed to more successful adaptability of human collectives at early stages of the development of society. The transition to agriculture, coupled with substantially increasing population density, was marked by the emergence and institutionalisation of social inequality based on the inequality of tangible assets and symbolic wealth. Then, new institutions of warfare came into existence, and they were aimed at conquering and enslaving the neighbours engaged in productive labour. While exercising control over nature, people also established and strengthened their power over other people. Chiefdom as a new type of polity came into being. Elementary forms of power (political, economic and ideological) served as a basis for the formation of early states. The societies in those states were characterised by social inequality and cruelties, including slavery, mass violence and numerous victims. Nowadays, the old elementary forms of power that are inherent in personalistic chiefdom are still functioning along with modern institutions of public and private bureaucracy. This constitutes the key contradiction of our time, which is the juxtaposition of individual despotic power and public infrastructural one. However, society is evolving towards an ever more efficient combination of social initiatives with the sustainability and viability of large-scale organisations.

Solution of Inverse Problems in Thermal Systems

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Yogesh Jaluria
Keyword(s):  
Heat Treatment ◽  
Inverse Problems ◽  
Initial Conditions ◽  
Optimization Methods ◽  
Small Region ◽  
Temperature Cycle ◽  
Unknown Boundary ◽  
Thermal Systems ◽  
Data Points ◽  
Unknown Boundary Conditions

Abstract A common occurrence in many practical systems is that the desired result is known or given, but the conditions needed for achieving this result are not known. This situation leads to inverse problems, which are of particular interest in thermal processes. For instance, the temperature cycle to which a component must be subjected in order to obtain desired characteristics in a manufacturing system, such as heat treatment or plastic thermoforming, is prescribed. However, the necessary boundary and initial conditions are not known and must be determined by solving the inverse problem. Similarly, an inverse solution may be needed to complete a given physical problem by determining the unknown boundary conditions. Solutions thus obtained are not unique and optimization is generally needed to obtain results within a small region of uncertainty. This review paper discusses several inverse problems that arise in a variety of practical processes and presents some of the approaches that may be used to solve them and obtain acceptable and realistic results. Optimization methods that may be used for reducing the error are presented. A few examples are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. These examples include the heat treatment process, unknown wall temperature distribution in a furnace, and transport in a plume or jet involving the determination of the strength and location of the heat source by employing a few selected data points downstream. Optimization of the positioning of the data points is used to minimize the number of samples needed for accurate predictions.

An object-oriented optimization framework for large-scale inverse problems

2021 ◽  
pp. 104790
Author(s):  
Ettore Biondi ◽  
Guillaume Barnier ◽  
Robert G. Clapp ◽  
Francesco Picetti ◽  
Stuart Farris
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Object Oriented ◽  
Optimization Framework

scholarly journals Arabidopsis Genes Essential for Seedling Viability: Isolation of Insertional Mutants and Molecular Cloning

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1765-1778
Author(s):  
Gregory J Budziszewski ◽  
Sharon Potter Lewis ◽  
Lyn Wegrich Glover ◽  
Jennifer Reineke ◽  
Gary Jones ◽  
...  
Keyword(s):  
Large Scale ◽  
Protein Translocation ◽  
Gene Families ◽  
Mutant Phenotype ◽  
Lethal Mutant ◽  
A Genome ◽  
Genes Encoding ◽  
High Level ◽  
Mutant Lines ◽  
Genome Scale

Abstract We have undertaken a large-scale genetic screen to identify genes with a seedling-lethal mutant phenotype. From screening ~38,000 insertional mutant lines, we identified >500 seedling-lethal mutants, completed cosegregation analysis of the insertion and the lethal phenotype for >200 mutants, molecularly characterized 54 mutants, and provided a detailed description for 22 of them. Most of the seedling-lethal mutants seem to affect chloroplast function because they display altered pigmentation and affect genes encoding proteins predicted to have chloroplast localization. Although a high level of functional redundancy in Arabidopsis might be expected because 65% of genes are members of gene families, we found that 41% of the essential genes found in this study are members of Arabidopsis gene families. In addition, we isolated several interesting classes of mutants and genes. We found three mutants in the recently discovered nonmevalonate isoprenoid biosynthetic pathway and mutants disrupting genes similar to Tic40 and tatC, which are likely to be involved in chloroplast protein translocation. Finally, we directly compared T-DNA and Ac/Ds transposon mutagenesis methods in Arabidopsis on a genome scale. In each population, we found only about one-third of the insertion mutations cosegregated with a mutant phenotype.

scholarly journals Influence of Wind Power on Modeling of Bidding Strategy in a Promising Power Market with a Modified Gravitational Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4438
Author(s):  
Satyendra Singh ◽  
Manoj Fozdar ◽  
Hasmat Malik ◽  
Maria del Valle Fernández Moreno ◽  
Fausto Pedro García Márquez
Keyword(s):  
Wind Power ◽  
Electricity Market ◽  
Large Scale ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Optimization Methods ◽  
Bidding Strategy ◽  
Wind Speed Profile ◽  
Gravitational Search ◽  
Modified Gravitational Search Algorithm

It is expected that large-scale producers of wind energy will become dominant players in the future electricity market. However, wind power output is irregular in nature and it is subjected to numerous fluctuations. Due to the effect on the production of wind power, producing a detailed bidding strategy is becoming more complicated in the industry. Therefore, in view of these uncertainties, a competitive bidding approach in a pool-based day-ahead energy marketplace is formulated in this paper for traditional generation with wind power utilities. The profit of the generating utility is optimized by the modified gravitational search algorithm, and the Weibull distribution function is employed to represent the stochastic properties of wind speed profile. The method proposed is being investigated and simplified for the IEEE-30 and IEEE-57 frameworks. The results were compared with the results obtained with other optimization methods to validate the approach.

New Harvesting and Curing Techniques in the Production of Breeder's Seed Peanuts1

1979 ◽  
Vol 6 (2) ◽  
pp. 70-72
Author(s):  
T. A. Coffelt ◽  
F. S. Wright ◽  
J. L. Steele
Keyword(s):  
Large Scale ◽  
Combine Method ◽  
Frost Damage ◽  
New Method ◽  
Experimental Equipment ◽  
Harvesting Method ◽  
Curing Methods ◽  
Labor Requirements ◽  
High Level ◽  
Varietal Purity

Abstract A new method of harvesting and curing breeder's seed peanuts in Virginia was initiated that would 1) reduce the labor requirements, 2) maintain a high level of germination, 3) maintain varietal purity at 100%, and 4) reduce the risk of frost damage. Three possible harvesting and curing methods were studied. The traditional stack-pole method satisfied the latter 3 objectives, but not the first. The windrow-combine method satisfied the first 2 objectives, but not the last 2. The direct harvesting method satisfied all four objectives. The experimental equipment and curing procedures for direct harvesting had been developed but not tested on a large scale for seed harvesting. This method has been used in Virginia to produce breeder's seed of 3 peanut varieties (Florigiant, VA 72R and VA 61R) during five years. Compared to the stackpole method, labor requirements have been reduced, satisfactory levels of germination and varietal purity have been obtained, and the risk of frost damage has been minimized.

scholarly journals Multi-task learning based Encoder-Decoder: A comprehensive detection and diagnosis system for multi-sensor data

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110131
Author(s):  
Junfeng Wu ◽  
Li Yao ◽  
Bin Liu ◽  
Zheyuan Ding ◽  
Lei Zhang
Keyword(s):  
Anomaly Detection ◽  
Event Detection ◽  
Large Scale ◽  
Multivariate Time Series ◽  
Sensor Data ◽  
Unified Framework ◽  
Diagnosis System ◽  
Learning Framework ◽  
Task Learning ◽  
Detection And Diagnosis

As more and more sensor data have been collected, automated detection, and diagnosis systems are urgently needed to lessen the increasing monitoring burden and reduce the risk of system faults. A plethora of researches have been done on anomaly detection, event detection, anomaly diagnosis respectively. However, none of current approaches can explore all these respects in one unified framework. In this work, a Multi-Task Learning based Encoder-Decoder (MTLED) which can simultaneously detect anomalies, diagnose anomalies, and detect events is proposed. In MTLED, feature matrix is introduced so that features are extracted for each time point and point-wise anomaly detection can be realized in an end-to-end way. Anomaly diagnosis and event detection share the same feature matrix with anomaly detection in the multi-task learning framework and also provide important information for system monitoring. To train such a comprehensive detection and diagnosis system, a large-scale multivariate time series dataset which contains anomalies of multiple types is generated with simulation tools. Extensive experiments on the synthetic dataset verify the effectiveness of MTLED and its multi-task learning framework, and the evaluation on a real-world dataset demonstrates that MTLED can be used in other application scenarios through transfer learning.

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