In this paper we describe a new approach to shar p boundary geophy sical inversion. We demon strate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonl inear parametrization of the mode l parameters. Thi s parametrization plays the same role as transformation into the space of the weighted model parameters, introd uced in the origi nal papers on focusing inversion. It allows us to transform the nonq uadrati c minim um support stabilizer into the traditional quadrati c minimum norm stabilizer, which simplifies the solution of the inverse problem. Thi s tran sformation automatically ensures that the solution belon gs to the class of model s with a minimum support. The method is illustrated with synthetic examples of 3D magnetotell uric inversion for an earth conductivity structure. To simplify the calculations, in the initial stage of the iterative inversion we use the quasi-analytic al approximation developed by Zhdanov and Hursan (2000 Inverse Problems 16 1297-322). However, to increase the accura cy of inversion, we apply rigorou s forward modelling based on the integral equa tion method at the final stage of the inversion. To obtain a stable solution of a 3D inverse problem , we use the Tikhonov regularization method with a new nonli near param etri zation. Thi s techn ique leads to the generation of a shar p image of anomalous condu ctiv ity distribution. The inversion is based on the regularized conju gate gradient method .

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Dynamical systems comprised of autonomous agents arise in many relevant problems such as multi-agent robotics, smart grids, or smart cities. Controlling these systems is of paramount importance to guarantee a successful deployment. Optimal centralized controllers are readily available but face limitations in terms of scalability and practical implementation. Optimal decentralized controllers, on the other hand, are difficult to find. In this paper we use graph neural networks (GNNs) to learn decentralized controllers from data. GNNs are well-suited for the task, since they are naturally distributed architectures. Furthermore, they are equivariant and stable, leading to good scalability and transferability properties. The problem of flocking is explored to illustrate the power of GNNs in learning decentralized controllers.

Interactive driving scenarios, such as lane changes, merges and unprotected turns, are some of the most challenging situations for autonomous driving. Planning in interactive scenarios requires accurately modeling the reactions of other agents to different future actions of the ego agent. We develop end-to-end models for conditional behavior prediction (CBP) that take as an input a query future trajectory for an egoagent, and predict distributions over future trajectories for other agents conditioned on the query. Leveraging such a model, we develop a general-purpose agent interactivity score derived from probabilistic first principles. The interactivity score allows us to find interesting interactive scenarios for training and evaluating behavior prediction models. We further demonstrate that the proposed score is effective for agent prioritization under computational budget constraints.

The existing techniques for appraisal of geophysical inverse images are based on calculating the model resolution and the model covariance matrices. In some applications, however, it becomes desirable to evaluate the upper bounds of the variations in the solution of the inverse problem. It is possible to use the Cauchy inequality for the regularized least-squares inversion to quantify the ability of an experiment to discriminate between two similar models in the presence of noise in the data. We present a new method for resolution analysis based on evaluating the spatial distribution of the upper bounds of the model variations and introduce a new characteristic of geophysical inversion, resolution density, as an inverse of these upper bounds. We derive an efficient numerical technique to compute the resolution density based on the spectral Lanczos decomposition method (SLDM). The methodology was tested on 3D synthetic linear and nonlinear electromagnetic (EM) data inversions, and also to interpret the helicopter-borne EM data collected by INCO Exploration in the Voisey’s Bay area of Canada.