Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Interrogation Theory

The goal of an investigation, scientific or otherwise, is usually to find answers to some specific set of questions about the state of nature: what is the seismic velocity structure? How likely is this volcano to erupt within a certain period? Does a subsurface reservoir contain resources of interest? Background research may reveal the existence of pertinent knowledge and information discovered previously, new data are normally acquired, and an inference problem is solved in order to answer the questions taking both all of the a priori information and the new data into account. Inverse theory, decision theory and the theory of experimental design provide methods to optimize the design of the investigation and to estimate results. However, those theories are normally set in the context of a particular model of the universe, with its particular parametrization. This requires the investigator to specify a priori a coherent utility (a function that describes the risks and rewards) of all possible outcomes under that parametrization. Quite commonly, the investigator may not be able to do this. Ideally an investigator would be able merely to pose a set of questions, define a set of constraints on the data types, acquisition costs and logistics, and provide a functional to relate the questions to any particular parameter space. Theory and methodology would then semi-autonomously drive the interrogation of the state of nature by optimally selecting one or more relevant models and parameter spaces, and designing, acquiring and analysing data, in order to best answer the questions. If necessary this could be done in a sequential or iterative manner, which potentially then involves changing the questions posed in each iteration based on both previous results and inspiration from the investigator. We present such a theory of interrogation in this paper. We review the relevant aspects of decision and design theory, and cast them in a framework where the investigator specifies a utility only at the level required by the general questions to be posed. Each model under consideration is then mapped into this utility space of possible answers. We then extend this framework to sequential investigations, where the outcome of each step may affect all aspects of the problem: the models entertained, the utilities and even the questions themselves. A variety of examples illustrates the generality of this method: an asset team investigating how best to exploit a subsurface reservoir, Monte Carlo sampling to estimate the Bayesian evidence for geophysical models, discriminating between different rock physics models of strain in laboratory deformation experiments, an organization sequentially assessing the effectiveness of its methods to evaluate subsurface assets, assessing whether subsurface CO₂ storage should be promoted for climate change mitigation, and examples running through the text of seismic tomography, earthquake characterization and autonomous interplanetary robotic exploration.ISSN:0956-540XISSN:1365-246

Improved dynamical particle swarm optimization method for structural dynamics

A methodology to the multiobjective structural design of buildings based on an improved particle swarm optimization algorithm is presented, which has proved to be very efficient and robust in nonlinear problems and when the optimization objectives are in conflict. In particular, the behaviour of the particle swarm optimization (PSO) classical algorithm is improved by dynamically adding autoadaptive mechanisms that enhance the exploration/exploitation trade-off and diversity of the proposed algorithm, avoiding getting trapped in local minima. A novel integrated optimization system was developed, called DI-PSO, to solve this problem which is able to control and even improve the structural behaviour under seismic excitations. In order to demonstrate the effectiveness of the proposed approach, the methodology is tested against some benchmark problems. Then a 3-story-building model is optimized under different objective cases, concluding that the improved multiobjective optimization methodology using DI-PSO is more efficient as compared with those designs obtained using single optimization.Peer ReviewedPostprint (published version

A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop \emph{Optimal Concentration Inequalities} (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository Research Papers). See SIAM Review for higher quality figure