Abstract: One of the critical issues when adopting Bayesian networks (BNs) to model dependencies among random variables is to “learn” their structure. This is a well-known NP-hard problem in its most general and classical formulation, which is furthermore complicated by known pitfalls such as the issue of I-equivalence among different structures. In this work we restrict the investigation to a specific class of networks, i.e., those representing the dynamics of phenomena characterized by the monotonic accumulation of events. Such phenomena allow to set specific structural constraints based on Suppes’ theory of probabilistic causation and, accordingly, to define constrained BNs, named Suppes-Bayes Causal Networks (SBCNs). Within this framework, we study the structure learning of SBCNs via extensive simulations with various state-of-the-art search strategies, such as canonical local search techniques and Genetic Algorithms. This investigation is intended to be an extension and an in-depth clarification of our previous works on SBCN structure learning. Among the main results, we show that Suppes’ constraints do simplify the learning task, by reducing the solution search space and providing a temporal ordering on the variables, which simplifies the complications derived by I-equivalent structures. Finally, we report on tradeoffs among different optimization techniques that can be used to learn SBCNs.

Abstract: We focus on a surface evolution problem where the local surface speed depends on a computationally expensive scalar function with non-local properties. The local surface speed must be re-evaluated in each time step, even for non-moving parts of the surface, due to possibly changed properties in remote regions of the simulation domain. We present a method to evaluate the surface speed only on a sparse set of points to reduce the computational effort. This sparse set of points is generated according to application-specific requirements using an iterative partitioning scheme. We diffuse the result of a constant extrapolation in the neighborhood of the sparse points to obtain an approximation to a linear interpolation between the sparse points. We demonstrate the method for a surface evolving with a local surface speed depending on the incident flux from a source plane above the surface. The obtained speedups range from 2 to 8 and the surface deviation is less than 3 grid-cells for all evaluated test cases.

Abstract: We propose a methodology to generate an accurate and efficient reconstruction of radiated fields based on high order interpolation. As the solution is obtained with the convolution by a smooth but potentially high frequency oscillatory kernel, our basis functions therefore incorporate plane waves. Directional interpolation is shown to be efficient for smart directions. An adaptive subdivision of the domain is established to limit the oscillations of the kernel in each element. The new basis functions, combining high order polynomials and plane waves, provide much better accuracy than low order ones. Finally, as standard visualization softwares are generally unable to represent such fields, a method to have a well-suited visualization of high order functions is used. Several numerical results confirm the potential of the method.

Abstract: In the paper we present a case study of the aero-structural analysis and optimization for the wing design using the modular analysis and unified derivatives (MAUD). Wing design is one of the essential procedures of aircraft manufactures and it is a compromise between many competing factors and constraints. As a result, the efficient numerical optimized methods are important to speed-up the design procedures special for the the design parameter of order~$\cal O$(10-100). In the aero-structural optimization, the derivatives can be calculated by simply applying the finite-difference methods. However, the finite difference methods are in general significantly more expensive, requiring at least one additional flow solution per parameter. By using the method of modular analysis and unified derivatives (MAUD), we can unify all methods for computing total derivatives using a single equation. The derivatives can be automatically uniform calculated [1]as \frac{\partial R}{\partial u} \frac{du}{dr} =\Psi = \frac{\partial R^T}{\partial u}\frac{du^T}{dr} The wing design requires a set of benchmark cases for the shape optimization. In the paper, we choice the Common Research Model (CRM) geometry which was developed by NASA Langely Research Center and Amers Research Center for applied CFD validation studies. In this paper we only focus on preliminary designs on the static aeroelastic analysis for example the aileron reversal analysis [2]. We use the open source code OpenMDAO [3] as the framework for the implementation of MAUD applied for the wing design. OpenMDAO provides a library of sparse solvers and optimizers designed to work with its distributed-memory, sparse data-passing scheme. We present performance comparisons for a typical production problem and a summary of the experiences gained. References: [1] J. R. R. A. Martins and J. T. Hwang, Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models, AIAA Journal, 51(1):2582--2599, 2013 [2] Mengmeng Zhang, Contributions to Variable Fidelity MDO Framework for Collaborative and Integrated Aircraft Design, Doctoral Thesis, Royal Institute of Technology KTH, Stockholm, Sweden, 2015. [3] OpenMDAO, http://openmdao.org/